Sample records for fast poisson solvers

We present a fast, direct and adaptive Poissonsolver for complex two-dimensional geometries based on potential theory and fast multipole acceleration. More precisely, the solver relies on the standard decomposition of the solution as the sum of a volume integral to account for the source distribution and a layer potential to enforce the desired boundary condition. The volume integral is computed by applying the FMM on a square box that encloses the domain of interest. For the sake of efficiency and convergence acceleration, we first extend the source distribution (the right-hand side in the Poisson equation) to the enclosing box as a C0 function using a fast, boundary integral-based method. We demonstrate on multiply connected domains with irregular boundaries that this continuous extension leads to high accuracy without excessive adaptive refinement near the boundary and, as a result, to an extremely efficient ;black box; fastsolver.

Direct numerical simulation (DNS) of high Reynolds number, Re >= O (105) , turbulent flows requires computational meshes >= O (1012) grid points, and, thus, the use of petascale supercomputers. DNS often requires the solution of a Helmholtz (or Poisson) equation for pressure, which constitutes the bottleneck of the solver. We have developed a parallel solver of the Helmholtz equation in 3D, PSH3D. The numerical method underlying PSH3D combines a parallel 2D Fast Fourier transform in two spatial directions, and a parallel linear solver in the third direction. For computational meshes up to 81923 grid points, our numerical results show that PSH3D scales up to at least 262k cores of Cray XT5 (Blue Waters). PSH3D has a peak performance 6 × faster than 3D FFT-based methods when used with the 'partial-global' optimization, and for a 81923 mesh solves the Poisson equation in 1 sec using 128k cores. Also, we have verified that the use of PSH3D with the 'partial-global' optimization in our DNS solver does not reduce the accuracy of the numerical solution of the incompressible Navier-Stokes equations.

FastPoissonsolvers using the Fast Fourier Transform on uniform grids are especially suited for parallel implementation, making them appropriate for portability on graphical processing unit (GPU) devices. The goal of the following work was to implement, test, and evaluate a fastPoissonsolver for periodic boundary conditions for use on a variety of GPU configurations. The solver used in this research was FLASH, an immersed-boundary-based method, which is well suited for complex, time-dependent geometries, has robust adaptive mesh refinement/de-refinement capabilities to capture evolving flow structures, and has been successfully implemented on conventional, parallel supercomputers. However, these solvers are still computationally costly to employ, and the total solver time is dominated by the solution of the pressure Poisson equation using state-of-the-art multigrid methods. FLASH improves the performance of its multigrid solvers by integrating a parallel FFT solver on a uniform grid during a coarse level. This hybrid solver could then be theoretically improved by replacing the highly-parallelizable FFT solver with one that utilizes GPUs, and, thus, was the motivation for my research. In the present work, the CPU-utilizing parallel FFT solver (PFFT) used in the base version of FLASH for solving the Poisson equation on uniform grids has been modified to enable parallel execution on CUDA-enabled GPU devices. New algorithms have been implemented to replace the Poissonsolver that decompose the computational domain and send each new block to a GPU for parallel computation. One-dimensional (1-D) decomposition of the computational domain minimizes the amount of network traffic involved in this bandwidth-intensive computation by limiting the amount of all-to-all communication required between processes. Advanced techniques have been incorporated and implemented in a GPU-centric code design, while allowing end users the flexibility of parameter control at runtime in

A Fortran program package is introduced for rapid evaluation of the electrostatic potentials and forces in biomolecular systems modeled by the linearized Poisson-Boltzmann equation. The numerical solver utilizes a well-conditioned boundary integral equation (BIE) formulation, a node-patch discretization scheme, a Krylov subspace iterative solver package with reverse communication protocols, and an adaptive new version of the fast multipole method in which the exponential expansions are used to diagonalize the multipole-to-local translations. The program and its full description, as well as several closely related libraries and utility tools are available at http://lsec.cc.ac.cn/~lubz/afmpb.html and a mirror site at http://mccammon.ucsd.edu/. This paper is a brief summary of the program: the algorithms, the implementation and the usage. Restrictions: Only three or six significant digits options are provided in this version. Unusual features: Most of the codes are in Fortran77 style. Memory allocation functions from Fortran90 and above are used in a few subroutines. Additional comments: The current version of the codes is designed and written for single core/processor desktop machines. Check http://lsec.cc.ac.cn/lubz/afmpb.html for updates and changes. Running time: The running time varies with the number of discretized elements (N) in the system and their distributions. In most cases, it scales linearly as a function of N.

An adaptive Cartesian grid (ACG) concept is presented for the fast and robust numerical solution of the 3D Poisson-Boltzmann Equation (PBE) governing the electrostatic interactions of large-scale biomolecules and highly charged multi-biomolecular assemblies such as ribosomes and viruses. The ACG offers numerous advantages over competing grid topologies such as regular 3D lattices and unstructured grids. For very large biological molecules and multi-biomolecule assemblies, the total number of grid-points is several orders of magnitude less than that required in a conventional lattice grid used in the current PBE solvers thus allowing the end user to obtain accurate and stable nonlinear PBE solutions on a desktop computer. Compared to tetrahedral-based unstructured grids, ACG offers a simpler hierarchical grid structure, which is naturally suited to multigrid, relieves indirect addressing requirements and uses fewer neighboring nodes in the finite difference stencils. Construction of the ACG and determination of the dielectric/ionic maps are straightforward, fast and require minimal user intervention. Charge singularities are eliminated by reformulating the problem to produce the reaction field potential in the molecular interior and the total electrostatic potential in the exterior ionic solvent region. This approach minimizes grid-dependency and alleviates the need for fine grid spacing near atomic charge sites. The technical portion of this paper contains three parts. First, the ACG and its construction for general biomolecular geometries are described. Next, a discrete approximation to the PBE upon this mesh is derived. Finally, the overall solution procedure and multigrid implementation are summarized. Results obtained with the ACG-based PBE solver are presented for: (i) a low dielectric spherical cavity, containing interior point charges, embedded in a high dielectric ionic solvent – analytical solutions are available for this case, thus allowing rigorous

A three-dimensional (3D) Poissonsolver with longitudinal periodic and transverse open boundary conditions can have important applications in beam physics of particle accelerators. In this paper, we present a fast efficient method to solve the Poisson equation using a spectral finite-difference method. This method uses a computational domain that contains the charged particle beam only and has a computational complexity of $O(N_u(logN_{mode}))$, where $N_u$ is the total number of unknowns and $N_{mode}$ is the maximum number of longitudinal or azimuthal modes. This saves both the computational time and the memory usage by using an artificial boundary condition in a large extended computational domain.

A generalized gyrokinetic Poissonsolver has been developed, which employs local operations in the configuration space to compute the polarization density response. The new technique is based on the actual physical process of gyrophase-averaging. It is useful for nonlocal simulations using general geometry equilibrium. Since it utilizes local operations rather than the global ones such as FFT, the new method is most amenable to massively parallel algorithms.

The computational study of chemical reactions in complex, wet environments is critical for applications in many fields. It is often essential to study chemical reactions in the presence of applied electrochemical potentials, taking into account the non-trivial electrostatic screening coming from the solvent and the electrolytes. As a consequence, the electrostatic potential has to be found by solving the generalized Poisson and the Poisson-Boltzmann equations for neutral and ionic solutions, respectively. In the present work, solvers for both problems have been developed. A preconditioned conjugate gradient method has been implemented for the solution of the generalized Poisson equation and the linear regime of the Poisson-Boltzmann, allowing to solve iteratively the minimization problem with some ten iterations of the ordinary Poisson equation solver. In addition, a self-consistent procedure enables us to solve the non-linear Poisson-Boltzmann problem. Both solvers exhibit very high accuracy and parallel efficiency and allow for the treatment of periodic, free, and slab boundary conditions. The solver has been integrated into the BigDFT and Quantum-ESPRESSO electronic-structure packages and will be released as an independent program, suitable for integration in other codes.

We solve Poisson's equation in d=2,3 space dimensions by using a spectral method based on Fourier decomposition. The choice of the basis implies that Dirichlet boundary conditions on a box are satisfied. A Green's function-based procedure allows us to impose Dirichlet conditions on any smooth closed boundary, by doubling the computational complexity. The error introduced by the spectral truncation and the discretization of the charge distribution is evaluated by comparison with the exact solution, known in the case of elliptical symmetry. To this end boundary conditions on an equipotential ellipse (ellipsoid) are imposed on the numerical solution. Scaling laws for the error dependence on the number K of Fourier components for each space dimension and the number N of point charges used to simulate the charge distribution are presented and tested. A procedure to increase the accuracy of the method in the beam core region is briefly outlined.

as regularisation we document an increased convergence rate up to tenth order. The method however, can easily be extended well beyond the tenth order. To show the full extend of the method we present the special case of a spectrally ideal regularisation of the velocity formulated integration kernel, which achieves......This paper presents a high order method for solving the unbounded Poisson equation on a regular mesh using a Green’s function solution. The high order convergence was achieved by formulating mollified integration kernels, that were derived from a filter regularisation of the solution field...... or by performing the differentiation as a multiplication of the Fourier coefficients. In this way, differential operators such as the divergence or curl of the solution field could be solved to the same high order convergence without additional computational effort. The method was applied and validated using...

A high order method is presented for solving the Poisson equation subject to mixed free-space and periodic boundary conditions by using fast Fourier transforms (FFT). The high order convergence is achieved by deriving mollified Green’s functions from a high order regularization function which...... provides a correspondingly smooth solution to the Poisson equation.The high order regularization function may be obtained analogous to the approximate deconvolution method used in turbulence models and strongly relates to deblurring algorithms used in image processing. At first we show that the regularized...... by super-positioning an inter-mesh correction. For sufficiently smooth vector fields this multi-resolution correction can be achieved without the loss of convergence rate. An implementation of the multi-resolution solver in a two-dimensional re-meshed particle-mesh based vortex method is presented...

and the integration kernel. In this work we show an implementation of high order regularised integration kernels in the HE algorithm for the unbounded Poisson equation to formally achieve an arbitrary high order convergence. We further present a quantitative study of the convergence rate to give further insight......In mesh-free particle methods a high order solution to the unbounded Poisson equation is usually achieved by constructing regularised integration kernels for the Biot-Savart law. Here the singular, point particles are regularised using smoothed particles to obtain an accurate solution with an order...

We seek to improve on the conventional FFT-based algorithms for solving the Poisson equation with infinite-domain (open) boundary conditions for large problems in accelerator modeling and related areas. In particular, improvements in both accuracy and performance are possible by combining several technologies: the method of local corrections (MLC); the James algorithm; and adaptive mesh refinement (AMR). The MLC enables the parallelization (by domain decomposition) of problems with large domains and many grid points. This improves on the FFT-based Poissonsolvers typically used as it doesn't require the all-to-all communication pattern that parallel 3d FFT algorithms require, which tends to be a performance bottleneck on current (and foreseeable) parallel computers. In initial tests, good scalability up to 1000 processors has been demonstrated for our new MLC solver. An essential component of our approach is a new version of the James algorithm for infinite-domain boundary conditions for the case of three dimensions. By using a simplified version of the fast multipole method in the boundary-to-boundary potential calculation, we improve on the performance of the Hockney algorithm typically used by reducing the number of grid points by a factor of 8, and the CPU costs by a factor of 3. This is particularly important for large problems where computer memory limits are a consideration. The MLC allows for the use of adaptive mesh refinement, which reduces the number of grid points and increases the accuracy in the Poisson solution. This improves on the uniform grid methods typically used in PIC codes, particularly in beam problems where the halo is large. Also, the number of particles per cell can be controlled more closely with adaptivity than with a uniform grid. To use AMR with particles is more complicated than using uniform grids. It affects depositing particles on the non-uniform grid, reassigning particles when the adaptive grid changes and maintaining the

We describe an implementation to solve Poisson's equation for an isolated system on a unigrid mesh using FFTs. The method solves the equation globally on mesh blocks distributed across multiple processes on a distributed-memory parallel computer. Test results to demonstrate the convergence and scaling properties of the implementation are presented. The solver is offered to interested users as the library PSPFFT.

In this paper, we present a GPU-accelerated direct-sum boundary integral method to solve the linear Poisson-Boltzmann (PB) equation. In our method, a well-posed boundary integral formulation is used to ensure the fast convergence of Krylov subspace based linear algebraic solver such as the GMRES. The molecular surfaces are discretized with flat triangles and centroid collocation. To speed up our method, we take advantage of the parallel nature of the boundary integral formulation and parallelize the schemes within CUDA shared memory architecture on GPU. The schemes use only $11N+6N_c$ size-of-double device memory for a biomolecule with $N$ triangular surface elements and $N_c$ partial charges. Numerical tests of these schemes show well-maintained accuracy and fast convergence. The GPU implementation using one GPU card (Nvidia Tesla M2070) achieves 120-150X speed-up to the implementation using one CPU (Intel L5640 2.27GHz). With our approach, solving PB equations on well-discretized molecular surfaces with up ...

This review outlines the recent progress made in developing more accurate and efficient solutions to model electrostatics in systems comprised of bio-macromolecules and nano-objects, the last one referring to objects that do not have biological function themselves but nowadays are frequently used in biophysical and medical approaches in conjunction with bio-macromolecules. The problem of modeling macromolecular electrostatics is reviewed from two different angles: as a mathematical task provided the specific definition of the system to be modeled and as a physical problem aiming to better capture the phenomena occurring in the real experiments. In addition, specific attention is paid to methods to extend the capabilities of the existing solvers to model large systems toward applications of calculations of the electrostatic potential and energies in molecular motors, mitochondria complex, photosynthetic machinery and systems involving large nano-objects. PMID:24199185

This review outlines the recent progress made in developing more accurate and efficient solutions to model electrostatics in systems comprised of bio-macromolecules and nano-objects, the last one referring to objects that do not have biological function themselves but nowadays are frequently used in biophysical and medical approaches in conjunction with bio-macromolecules. The problem of modeling macromolecular electrostatics is reviewed from two different angles: as a mathematical task provided the specific definition of the system to be modeled and as a physical problem aiming to better capture the phenomena occurring in the real experiments. In addition, specific attention is paid to methods to extend the capabilities of the existing solvers to model large systems toward applications of calculations of the electrostatic potential and energies in molecular motors, mitochondria complex, photosynthetic machinery and systems involving large nano-objects.

Quantum Monte Carlo (QMC) is an extremely powerful method to treat many-body systems. Usually quantum Monte Carlo has been applied in cases where the interaction potential has a simple analytic form, like the 1/r Coulomb potential. However, in a complicated environment as in a semiconductor heterostructure, the evaluation of the interaction itself becomes a non-trivial problem. Obtaining the potential from any grid-based finite-difference method, for every walker and every step is unfeasible. We demonstrate an alternative approach of solving the Poisson equation by a classical Monte Carlo within the overall quantum Monte Carlo scheme. We have developed a modified ''Walk On Spheres'' algorithm using Green's function techniques, which can efficiently account for the interaction energy of walker configurations, typical of quantum Monte Carlo algorithms. This stochastically obtained potential can be easily incorporated within popular quantum Monte Carlo techniques like variational Monte Carlo (VMC) or diffusion Monte Carlo (DMC). We demonstrate the validity of this method by studying a simple problem, the polarization of a helium atom in the electric field of an infinite capacitor.

We present an analysis of different methods to calculate the classical electrostatic Hartree potential created by charge distributions. Our goal is to provide the reader with an estimation on the performance ---in terms of both numerical complexity and accuracy--- of popular Poissonsolvers, and to give an intuitive idea on the way these solvers operate. Highly parallelisable routines have been implemented in the first-principle simulation code Octopus to be used in our tests, so that reliable conclusions about the capability of methods to tackle large systems in cluster computing can be obtained from our work.

This paper describes a powerful and simple new wavelet-based preconditioning method for the CG solvers of Poisson equation. The equation can be solved with an iterative matrix solver, however, in the absence of our method, the computing time will increase exponentially with respect to an increase in grid points. Use of our technique leads to a matrix with a bounded condition number so that computing time is reduced significantly. Results from our numerical experiments confirm the power and accuracy of our wavelet-based preconditioning method. Unlike many preconditioning methods which are not suitable for vector and parallel processing, our algorithm can take advantage of the extra processing capabilities and enhance computing performance. For example, a speed up of over 100 fold can be achieved when solving Poisson equations on a Cray T3D using 128 processors in parallel. (author)

We present the open source distributed software package Poisson-Boltzmann Analytical Method (PB-AM), a fully analytical solution to the linearized Poisson Boltzmann equation. The PB-AM software package includes the generation of outputs files appropriate for visualization using VMD, a Brownian dynamics scheme that uses periodic boundary conditions to simulate dynamics, the ability to specify docking criteria, and offers two different kinetics schemes to evaluate biomolecular association rate constants. Given that PB-AM defines mutual polarization completely and accurately, it can be refactored as a many-body expansion to explore 2- and 3-body polarization. Additionally, the software has been integrated into the Adaptive Poisson-Boltzmann Solver (APBS) software package to make it more accessible to a larger group of scientists, educators and students that are more familiar with the APBS framework.

The Poisson-Boltzmann (PB) formalism is among the most popular approaches to modeling the solvation of molecules. It assumes a continuum model for water, leading to a dielectric permittivity that only depends on position in space. In contrast, the dipolar Poisson-Boltzmann-Langevin (DPBL) formalism represents the solvent as a collection of orientable dipoles with nonuniform concentration; this leads to a nonlinear permittivity function that depends both on the position and on the local electric field at that position. The differences in the assumptions underlying these two models lead to significant differences in the equations they generate. The PB equation is a second order, elliptic, nonlinear partial differential equation (PDE). Its response coefficients correspond to the dielectric permittivity and are therefore constant within each subdomain of the system considered (i.e., inside and outside of the molecules considered). While the DPBL equation is also a second order, elliptic, nonlinear PDE, its response coefficients are nonlinear functions of the electrostatic potential. Many solvers have been developed for the PB equation; to our knowledge, none of these can be directly applied to the DPBL equation. The methods they use may adapt to the difference; their implementations however are PBE specific. We adapted the PBE solver originally developed by Holst and Saied [J. Comput. Chem. 16, 337 (1995)] to the problem of solving the DPBL equation. This solver uses a truncated Newton method with a multigrid preconditioner. Numerical evidences suggest that it converges for the DPBL equation and that the convergence is superlinear. It is found however to be slow and greedy in memory requirement for problems commonly encountered in computational biology and computational chemistry. To circumvent these problems, we propose two variants, a quasi-Newton solver based on a simplified, inexact Jacobian and an iterative self-consistent solver that is based directly on the PBE

A new fast direct linear equation solver for the boundary element method (BEM) is presented in this paper. The idea of the new fast direct solver stems from the concept of the hierarchical off-diagonal low-rank matrix. The hierarchical off-diagonal low-rank matrix can be decomposed into the multiplication of several diagonal block matrices. The inverse of the hierarchical off-diagonal low-rank matrix can be calculated efficiently with the Sherman-Morrison-Woodbury formula. In this paper, a more general and efficient approach to approximate the coefficient matrix of the BEM with the hierarchical off-diagonal low-rank matrix is proposed. Compared to the current fast direct solver based on the hierarchical off-diagonal low-rank matrix, the proposed method is suitable for solving general 3-D boundary element models. Several numerical examples of 3-D potential problems with the total number of unknowns up to above 200,000 are presented. The results show that the new fast direct solver can be applied to solve large 3-D BEM models accurately and with better efficiency compared with the conventional BEM.

Rail transportation plays an important role in our everyday life, and there is fast development and modernization in the railway industry to meet the growing demand for swifter, safer and more comfortable trains. At the same time, the security of train operation and the maintenance of rails have to

In this note we propose an approach for a fast analytic determination of all possible sets of Bethe roots corresponding to eigenstates of rational {GL}({N}\\vert {M}) integrable spin chains of given not too large length, in terms of Baxter Q-functions. We observe that all exceptional solutions, if any, are automatically correctly accounted. The key intuition behind the approach is that the equations on the Q-functions are determined solely by the Young diagram, and not by the choice of the rank of the {GL} symmetry. Hence we can choose arbitrary {N} and {M} that accommodate the desired representation. Then we consider all distinguished Q-functions at once, not only those following a certain Kac-Dynkin path.

In this note we propose an approach for a fast analytic determination of all possible eigenstates of rational GL(N|M) integrable spin chains of given not too large length, in terms of Baxter Q-functions. We observe that all exceptional solutions, if any, are automatically correctly accounted. The key intuition behind the approach is that the equations on the Q-functions are determined solely by the Young diagram, and not by the choice of the rank of the GL symmetry. Hence we can choose arbitrary N and M that accommodate the desired representation. Then we consider all distinguished Q-functions at once, not only those following a certain Kac-Dynkin path.

Resolving numerically Vlasov-Poisson equations for initially cold systems can be reduced to following the evolution of a three-dimensional sheet evolving in six-dimensional phase-space. We describe a public parallel numerical algorithm consisting in representing the phase-space sheet with a conforming, self-adaptive simplicial tessellation of which the vertices follow the Lagrangian equations of motion. The algorithm is implemented both in six- and four-dimensional phase-space. Refinement of the tessellation mesh is performed using the bisection method and a local representation of the phase-space sheet at second order relying on additional tracers created when needed at runtime. In order to preserve in the best way the Hamiltonian nature of the system, refinement is anisotropic and constrained by measurements of local Poincaré invariants. Resolution of Poisson equation is performed using the fast Fourier method on a regular rectangular grid, similarly to particle in cells codes. To compute the density projected onto this grid, the intersection of the tessellation and the grid is calculated using the method of Franklin and Kankanhalli [65-67] generalised to linear order. As preliminary tests of the code, we study in four dimensional phase-space the evolution of an initially small patch in a chaotic potential and the cosmological collapse of a fluctuation composed of two sinusoidal waves. We also perform a "warm" dark matter simulation in six-dimensional phase-space that we use to check the parallel scaling of the code.

Resolving numerically Vlasov-Poisson equations for initially cold systems can be reduced to following the evolution of a three-dimensional sheet evolving in six-dimensional phase-space. We describe a public parallel numerical algorithm consisting in representing the phase-space sheet with a conforming, self-adaptive simplicial tessellation of which the vertices follow the Lagrangian equations of motion. The algorithm is implemented both in six- and four-dimensional phase-space. Refinement of the tessellation mesh is performed using the bisection method and a local representation of the phase-space sheet at second order relying on additional tracers created when needed at runtime. In order to preserve in the best way the Hamiltonian nature of the system, refinement is anisotropic and constrained by measurements of local Poincar\\'e invariants. Resolution of Poisson equation is performed using the fast Fourier method on a regular rectangular grid, similarly to particle in cells codes. To compute the density proj...

Resolving numerically Vlasov–Poisson equations for initially cold systems can be reduced to following the evolution of a three-dimensional sheet evolving in six-dimensional phase-space. We describe a public parallel numerical algorithm consisting in representing the phase-space sheet with a conforming, self-adaptive simplicial tessellation of which the vertices follow the Lagrangian equations of motion. The algorithm is implemented both in six- and four-dimensional phase-space. Refinement of the tessellation mesh is performed using the bisection method and a local representation of the phase-space sheet at second order relying on additional tracers created when needed at runtime. In order to preserve in the best way the Hamiltonian nature of the system, refinement is anisotropic and constrained by measurements of local Poincaré invariants. Resolution of Poisson equation is performed using the fast Fourier method on a regular rectangular grid, similarly to particle in cells codes. To compute the density projected onto this grid, the intersection of the tessellation and the grid is calculated using the method of Franklin and Kankanhalli [65–67] generalised to linear order. As preliminary tests of the code, we study in four dimensional phase-space the evolution of an initially small patch in a chaotic potential and the cosmological collapse of a fluctuation composed of two sinusoidal waves. We also perform a “warm” dark matter simulation in six-dimensional phase-space that we use to check the parallel scaling of the code.

An unbinned statistical test on cluster-like deviations from Poisson processes for point process data is introduced, presented in the context of time variability analysis of astrophysical sources in count rate experiments. The measure of deviation of the actually obtained temporal event distribution from that of a Poisson process is derived from the distribution of time differences between two consecutive events in a natural way. The differential character of the measure suggests this test in particular for the search of irregular burst-like structures in experimental data. The construction allows the application of the test even for very low event numbers. Furthermore, the test can easily be applied in the case of varying acceptance of the detector as well. The simple and direct use of background events simultaneously acquired under the same conditions to account for acceptance variations is possible, allowing for easy application especially in earth-bound gamma-ray experiments. Central features are the fast...

A Matlab-based finite-difference numerical solver for the Poisson equation for a rectangle and a disk in two dimensions, and a spherical domain in three dimensions, is presented. The solver is optimized for handling an arbitrary combination of Dirichlet and Neumann boundary conditions, and allows for full user control of mesh refinement. The solver routines utilize effective and parallelized sparse vector and matrix operations. Computations exhibit high speeds, numerical stability with respect to mesh size and mesh refinement, and acceptable error values even on desktop computers. Catalogue identifier: AENQ_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AENQ_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU General Public License v3.0 No. of lines in distributed program, including test data, etc.: 102793 No. of bytes in distributed program, including test data, etc.: 369378 Distribution format: tar.gz Programming language: Matlab 2010a. Computer: PC, Macintosh. Operating system: Windows, OSX, Linux. RAM: 8 GB (8, 589, 934, 592 bytes) Classification: 4.3. Nature of problem: To solve the Poisson problem in a standard domain with “patchy surface”-type (strongly heterogeneous) Neumann/Dirichlet boundary conditions. Solution method: Finite difference with mesh refinement. Restrictions: Spherical domain in 3D; rectangular domain or a disk in 2D. Unusual features: Choice between mldivide/iterative solver for the solution of large system of linear algebraic equations that arise. Full user control of Neumann/Dirichlet boundary conditions and mesh refinement. Running time: Depending on the number of points taken and the geometry of the domain, the routine may take from less than a second to several hours to execute.

Exascale systems are predicted to have approximately one billion cores, assuming Gigahertz cores. Limitations on affordable network topologies for distributed memory systems of such massive scale bring new challenges to the currently dominant parallel programing model. Currently, there are many efforts to evaluate the hardware and software bottlenecks of exascale designs. It is therefore of interest to model application performance and to understand what changes need to be made to ensure extrapolated scalability. Fast multipole methods (FMM) were originally developed for accelerating N-body problems for particle-based methods in astrophysics and molecular dynamics. FMM is more than an N-body solver, however. Recent efforts to view the FMM as an elliptic PDE solver have opened the possibility to use it as a preconditioner for even a broader range of applications. In this thesis, we (i) discuss the challenges for FMM on current parallel computers and future exascale architectures, with a focus on inter-node communication, and develop a performance model that considers the communication patterns of the FMM for spatially quasi-uniform distributions, (ii) employ this performance model to guide performance and scaling improvement of FMM for all-atom molecular dynamics simulations of uniformly distributed particles, and (iii) demonstrate that, beyond its traditional use as a solver in problems for which explicit free-space kernel representations are available, the FMM has applicability as a preconditioner in finite domain elliptic boundary value problems, by equipping it with boundary integral capability for satisfying conditions at finite boundaries and by wrapping it in a Krylov method for extensibility to more general operators. Compared with multilevel methods, FMM is capable of comparable algebraic convergence rates down to the truncation error of the discretized PDE, and it has superior multicore and distributed memory scalability properties on commodity

Among optimal hierarchical algorithms for the computational solution of elliptic problems, the Fast Multipole Method (FMM) stands out for its adaptability to emerging architectures, having high arithmetic intensity, tunable accuracy, and relaxed global synchronization requirements. We demonstrate that, beyond its traditional use as a solver in problems for which explicit free-space kernel representations are available, the FMM has applicability as a preconditioner in finite domain elliptic boundary value problems, by equipping it with boundary integral capability for finite boundaries and by wrapping it in a Krylov method for extensibility to more general operators. Compared with multilevel methods, it is capable of comparable algebraic convergence rates down to the truncation error of the discretized PDE, and it has superior multicore and distributed memory scalability properties on commodity architecture supercomputers.

Laplacian matrices of graphs arise in large-scale computational applications such as machine learning; spectral clustering of images, genetic data and web pages; transportation network flows; electrical resistor circuits; and elliptic partial differential equations discretized on unstructured grids with finite elements. A Lean Algebraic Multigrid (LAMG) solver of the linear system Ax=b is presented, where A is a graph Laplacian. LAMG's run time and storage are linear in the number of graph edges. LAMG consists of a setup phase, in which a sequence of increasingly-coarser Laplacian systems is constructed, and an iterative solve phase using multigrid cycles. General graphs pose algorithmic challenges not encountered in traditional applications of algebraic multigrid. LAMG combines a lean piecewise-constant interpolation, judicious node aggregation based on a new node proximity definition, and an energy correction of the coarse-level systems. This results in fast convergence and substantial overhead and memory s...

The size-modified Poisson-Boltzmann equation (SMPBE) is one important variant of the popular dielectric model, the Poisson-Boltzmann equation (PBE), to reflect ionic size effects in the prediction of electrostatics for a biomolecule in an ionic solvent. In this paper, a new SMPBE hybrid solver is developed using a solution decomposition, the Schwartz's overlapped domain decomposition, finite element, and finite difference. It is then programmed as a software package in C, Fortran, and Python based on the state-of-the-art finite element library DOLFIN from the FEniCS project. This software package is well validated on a Born ball model with analytical solution and a dipole model with a known physical properties. Numerical results on six proteins with different net charges demonstrate its high performance. Finally, this new SMPBE hybrid solver is shown to be numerically stable and convergent in the calculation of electrostatic solvation free energy for 216 biomolecules and binding free energy for a DNA-drug com...

In order to compute polarization energy of biomolecules, we describe a boundary element approach to solving the linearized Poisson-Boltzmann equation. Our approach combines several important features including the derivative boundary formulation of the problem and a smooth approximation of the molecular surface based on the algebraic spline molecular surface. State of the art software for numerical linear algebra and the kernel independent fast multipole method is used for both simplicity and efficiency of our implementation. We perform a variety of computational experiments, testing our method on a number of actual proteins involved in molecular docking and demonstrating the effectiveness of our solver for computing molecular polarization energy. PMID:21660123

The nonlocal dielectric approach has been studied for more than forty years but only limited to water solvent until the recent work of Xie et al. (2013) [20]. As the development of this recent work, in this paper, a nonlocal modified Poisson-Boltzmann equation (NMPBE) is proposed to incorporate nonlocal dielectric effects into the classic Poisson-Boltzmann equation (PBE) for protein in ionic solvent. The focus of this paper is to present an efficient finite element algorithm and a related software package for solving NMPBE. Numerical results are reported to validate this new software package and demonstrate its high performance for protein molecules. They also show the potential of NMPBE as a better predictor of electrostatic solvation and binding free energies than PBE.

We present a new approach to find accurate solutions to the Poisson equation, as obtained from the steady-state limit of a diffusion equation with strong source terms. For this purpose, we start from Boltzmann's kinetic theory and investigate the influence of higher order terms on the resulting macroscopic equations. By performing an appropriate expansion of the equilibrium distribution, we provide a method to remove the unnecessary terms up to a desired order and show that it is possible to find, with high level of accuracy, the steady-state solution of the diffusion equation for sizeable Knudsen numbers. In order to test our kinetic approach, we discretise the Boltzmann equation and solve the Poisson equation, spending up to six order of magnitude less computational time for a given precision than standard lattice Boltzmann methods.

This paper presents the nonhomogeneous Poisson process (NHPP) for modeling the rate of fast radio bursts (FRBs) and other infrequently observed astronomical events. The NHPP, well-known in statistics, can model the dependence of the rate on both astronomical features and the details of an observing campaign. This is particularly helpful for rare events like FRBs because the NHPP can combine information across surveys, making the most of all available information. The goal of the paper is two-fold. First, it is intended to be a tutorial on the use of the NHPP. Second, we build an NHPP model that incorporates beam patterns and a power-law flux distribution for the rate of FRBs. Using information from 12 surveys including 15 detections, we find an all-sky FRB rate of 587 events per sky per day above a flux of 1 Jy (95% CI: 272, 924) and a flux power-law index of 0.91 (95% CI: 0.57, 1.25). Our rate is lower than other published rates, but consistent with the rate given in Champion et al.

Here we present a new particle-mesh galactic N-body code that uses the full multigrid algorithm for solving the modified Poisson equation of the Quasi Linear formulation of Modified Newtonian Dynamics (QUMOND). A novel approach for handling the boundary conditions using a refinement strategy is implemented and the accuracy of the code is compared with analytical solutions of Kuzmin disks. We then employ the code to compute the predicted rotation curves for a sample of five spiral galaxies from the THINGS sample. We generated static N-body realisations of the galaxies according to their stellar and gaseous surface densities and allowed their distances, mass-to-light ratios (M/L) and both the stellar and gas scale-heights to vary in order to estimate the best fit parameters. We found that NGC 3621, NGC 3521 and DDO 154 are well fit by MOND using expected values of the distance and M/L. NGC 2403 required a moderately larger $M/L$ than expected and NGC 2903 required a substantially larger value. The surprising re...

We present LAPACKrc, a family of FPGA-based linear algebra solvers able to achieve more than 100x speedup per commodity processor on certain problems. LAPACKrc subsumes some of the LAPACK and ScaLAPACK functionalities, and it also incorporates sparse direct and iterative matrix solvers. Current LAPACKrc prototypes demonstrate between 40x-150x speedup compared against top-of-the-line hardware/software systems. A technology roadmap is in place to validate current performance of LAPACKrc in HPC applications, and to increase the computational throughput by factors of hundreds within the next few years.

In this paper we develop a deterministic high order accurate finite-difference WENO solver to the solution of the 1-D Boltzmann-Poisson system for semiconductor devices. We follow the work in Fatemi and Odeh and in Majorana and Pidatella to formulate the Boltzmann-Poisson system in a spherical coordinate system using the energy as one of the coordinate variables, thus reducing the computational complexity to two dimensions in phase space and dramatically simplifying the evaluations of the collision terms. The solver is accurate in time hence potentially useful for time-dependent simulations, although in this paper we only test it for steady-state devices. The high order accuracy and nonoscillatory properties of the solver allow us to use very coarse meshes to get a satisfactory resolution, thus making it feasible to develop a 2-D solver (which will be five dimensional plus time when the phase space is discretized) on today's computers. The computational results have been compared with those by a Monte Carlo s...

As the fastest integral equation solver to date, the multilevel fast multipole algorithm (MLFMA)has been applied successfully to solve electromagnetic scattering and radiation from 3D electrically large objects.But for very large-scale problems, the storage and CPU time required in MLFMA are still expensive. Fast 3D electromagnetic scattering and radiation solvers are introduced based on MLFMA. A brief review of MLFMA is first given. Then, four fast methods including higher-order MLFMA (HO-MLFMA), fast far field approximation combined with adaptive ray propagation MLFMA (FAFFA-ARP-MLFMA), local MLFMA and parallel MLFMA are introduced. Some typical numerical results demonstrate the efficiency of these fast methods.

Full Text Available Knowledge about the electrostatic potential on the surface of biomolecules or biomembranes under physiological conditions is an important step in the attempt to characterize the physico-chemical properties of these molecules and in particular also their interactions with each other. Additionally, knowledge about solution electrostatics may guide also the design of molecules with specified properties. However, explicit water models come at a high computational cost, rendering them unsuitable for large design studies or for docking purposes. Implicit models with the water phase treated as a continuum require the numerical solution of the Poisson-Boltzmann Equation (PBE. Here, we present a new flexible program for the numerical solution of the PBE, allowing for different geometries, and the explicit and implicit inclusion of membranes. It involves a discretization of space and the computation of the molecular surface. The PBE is solved using finite differences, the resulting set of equations is solved using a Gauss-Seidel method. It is shown for the example of the sucrose transporter ScrY that the implicit inclusion of a surrounding membrane has a strong effect also on the electrostatics within the pore region and thus need to be carefully considered e.g. in design studies on membrane proteins.

Knowledge about the electrostatic potential on the surface of biomolecules or biomembranes under physiological conditions is an important step in the attempt to characterize the physico-chemical properties of these molecules and, in particular, also their interactions with each other. Additionally, knowledge about solution electrostatics may also guide the design of molecules with specified properties. However, explicit water models come at a high computational cost, rendering them unsuitable for large design studies or for docking purposes. Implicit models with the water phase treated as a continuum require the numerical solution of the Poisson-Boltzmann equation (PBE). Here, we present a new flexible program for the numerical solution of the PBE, allowing for different geometries, and the explicit and implicit inclusion of membranes. It involves a discretization of space and the computation of the molecular surface. The PBE is solved using finite differences, the resulting set of equations is solved using a Gauss-Seidel method. It is shown for the example of the sucrose transporter ScrY that the implicit inclusion of a surrounding membrane has a strong effect also on the electrostatics within the pore region and, thus, needs to be carefully considered, e.g., in design studies on membrane proteins.

alpha=0.5. Third, the most important test was performed on two types of real media that were used for previous studies. A fracture network measured by FIB/SEM in a low permeability sandstone was used for that purpose; the two dimensionless permeabilities KS and KL are equal to 9.3d-3 and 8.5d-3. Similar calculations were performed on 256 samples of Fontainebleau sandstones and the agreement was in general excellent, except may be for very low permeabilities. To conclude, the Laplace solver is significantly more stable than the lattice Boltzmann approach, uses less memory, and is significantly faster. Permeabilities are in excellent agreement over a wide range of porosities.

Obtaining pressure field data from particle image velocimetry (PIV) is an attractive technique in fluid dynamics due to its noninvasive nature. The application of this technique generally involves integrating the pressure gradient or solving the pressure Poisson equation using a velocity field measured with PIV. However, very little research has been done to investigate the dynamics of error propagation from PIV-based velocity measurements to the pressure field calculation. Rather than measure the error through experiment, we investigate the dynamics of the error propagation by examining the Poisson equation directly. We analytically quantify the error bound in the pressure field, and are able to illustrate the mathematical roots of why and how the Poisson equation based pressure calculation propagates error from the PIV data. The results show that the error depends on the shape and type of boundary conditions, the dimensions of the flow domain, and the flow type.

Obtaining pressure field data from particle image velocimetry (PIV) is an attractive technique in fluid dynamics due to its noninvasive nature. The application of this technique generally involves integrating the pressure gradient or solving the pressure Poisson equation using a velocity field measured with PIV. However, very little research has been done to investigate the dynamics of error propagation from PIV-based velocity measurements to the pressure field calculation. Rather than measure the error through experiment, we investigate the dynamics of the error propagation by examining the Poisson equation directly. We analytically quantify the error bound in the pressure field, and are able to illustrate the mathematical roots of why and how the Poisson equation based pressure calculation propagates error from the PIV data. The results show that the error depends on the shape and type of boundary conditions, the dimensions of the flow domain, and the flow type.

Obtaining pressure field data from particle image velocimetry (PIV) is an attractive technique in fluid dynamics due to its noninvasive nature. The application of this technique generally involves integrating the pressure gradient or solving the pressure Poisson equation using a velocity field measured with PIV. However, very little research has been done to investigate the dynamics of error propagation from PIV-based velocity measurements to the pressure field calculation. Rather than measure the error through experiment, we investigate the dynamics of the error propagation by examining the Poisson equation directly. We analytically quantify the error bound in the pressure field, and are able to illustrate the mathematical roots of why and how the Poisson equation based pressure calculation propagates error from the PIV data. The results show that the error depends on the shape and type of boundary conditions, the dimensions of the flow domain, and the flow type.

We present a fast and accurate algorithm for the Poisson equation in complex geometries, using regular Cartesian grids. We consider a variety of configurations, including Poisson equations with interfaces across which the solution is discontinuous (of the type arising in multi-fluid flows). The algorithm is based on a combination of the Correction Function Method (CFM) and Boundary Integral Methods (BIM). Interface and boundary conditions can be treated in a fast and accurate manner using boundary integral equations, and the associated BIM. Unfortunately, BIM can be costly when the solution is needed everywhere in a grid, e.g. fluid flow problems. We use the CFM to circumvent this issue. The solution from the BIM is used to rewrite the problem as a series of Poisson equations in rectangular domains --- which requires the BIM solution at interfaces/boundaries only. These Poisson equations involve discontinuities at interfaces, of the type that the CFM can handle. Hence we use the CFM to solve them (to high ord...

We present a new fastsolver to calculate fixed-boundary plasma equilibria in toroidally axisymmetric geometries. By combining conformal mapping with Fourier and integral equation methods on the unit disk, we show that high-order accuracy can be achieved for the solution of the equilibrium equation and its first and second derivatives. Smooth arbitrary plasma cross-sections as well as arbitrary pressure and poloidal current profiles are used as initial data for the solver. Equilibria with large Shafranov shifts can be computed without difficulty. Spectral convergence is demonstrated by comparing the numerical solution with a known exact analytic solution. A fusion-relevant example of an equilibrium with a pressure pedestal is also presented.

We analyze the accuracy of a 2D Poisson-Vlasov PIC integrator, taking the KV as a reference solution for a FODO cell. The particle evolution is symplectic and the Poissonsolver is based on FFT. The numerical error, evaluated by comparing the moments of the distribution and the electric field with the exact solution, shows a linear growth. This effect can be modeled by a white noise in the envelope equations for the KV beam. In order to investigate the collisional effects we have integrated the Hamilton's equations for N charged macro-particles with a hard-core r/sub H/ reducing the computational complexity to N/sup 3/2/. In the constant focusing case we observed that a KV beam, matched or mismatched relaxes to the Maxwell-Boltzmann self consistent distribution on a time interval, which depends on r/sub H/ and has a finite limit, for r/sub H/ to 0. A fully 3D PIC code for short bunches was developed for the ADS linac design at LNL (Italy). A 3D particle-core model, based on Langevin's equations with the drift...

Full Text Available A self-consistent Boltzmann-Poisson-Schrödinger solver for High Electron Mobility Transistor is presented. The quantization of electrons in the quantum well normal to the heterojunction is taken into account by solving the two higher moments of Boltzmann equation along with the Schrödinger and Poisson equations, self-consistently. The Boltzmann transport equation in the form of a current continuity equation and an energy balance equation are solved to obtain the transient and steady-state transport behavior. The numerical instability problems associated with the simulator are presented, and the criteria for smooth convergence of the solutions are discussed. The current-voltage characteristics, transconductance, gate capacitance, and unity-gain frequency of a single quantum well HEMT is discussed. It has been found that a HEMT device with a gate length of 0.7 μ m , and with a gate bias voltage of 0.625 V, has a transconductance of 579.2 mS/mm, which together with the gate capacitance of 19.28 pF/cm, can operate at a maximum unity-gain frequency of 47.8 GHz.

Full Text Available A self-consistent Boltzmann-Poisson-Schrödinger solver for High Electron Mobility Transistor is presented. The quantization of electrons in the quantum well normal to the heterojunction is taken into account by solving the two higher moments of Boltzmann equation along with the Schrödinger and Poisson equations, self-consistently. The Boltzmann transport equation in the form of a current continuity equation and an energy balance equation are solved to obtain the transient and steady-state transport behavior. The numerical instability problems associated with the simulator are presented, and the criteria for smooth convergence of the solutions are discussed. The current-voltage characteristics, transconductance, gate capacitance, and unity-gain frequency of a single quantum well HEMT is discussed. It has been found that a HEMT device with a gate length of 0.7 μm, and with a gate bias voltage of 0.625 V, has a transconductance of 579.2 mS/mm, which together with the gate capacitance of 19.28 pF/cm, can operate at a maximum unity-gain frequency of 47.8 GHz.

This dissertation introduces a novel fast direct solver and preconditioner for the solution of block tridiagonal linear systems that arise from the discretization of elliptic partial differential equations on a Cartesian product mesh, such as the variable-coefficient Poisson equation, the convection-diffusion equation, and the wave Helmholtz equation in heterogeneous media. The algorithm extends the traditional cyclic reduction method with hierarchical matrix techniques. The resulting method exposes substantial concurrency, and its arithmetic operations and memory consumption grow only log-linearly with problem size, assuming bounded rank of off-diagonal matrix blocks, even for problems with arbitrary coefficient structure. The method can be used as a standalone direct solver with tunable accuracy, or as a black-box preconditioner in conjunction with Krylov methods. The challenges that distinguish this work from other thrusts in this active field are the hybrid distributed-shared parallelism that can demonstrate the algorithm at large-scale, full three-dimensionality, and the three stressors of the current state-of-the-art multigrid technology: high wavenumber Helmholtz (indefiniteness), high Reynolds convection (nonsymmetry), and high contrast diffusion (inhomogeneity). Numerical experiments corroborate the robustness, accuracy, and complexity claims and provide a baseline of the performance and memory footprint by comparisons with competing approaches such as the multigrid solver hypre, and the STRUMPACK implementation of the multifrontal factorization with hierarchically semi-separable matrices. The companion implementation can utilize many thousands of cores of Shaheen, KAUST\\'s Haswell-based Cray XC-40 supercomputer, and compares favorably with other implementations of hierarchical solvers in terms of time-to-solution and memory consumption.

Full Text Available To meet the requirements of fast and automatic computation of subsonic and transonic aerodynamics in aircraft conceptual design, a novel finite volume solver for full potential flows on adaptive Cartesian grids is developed in this paper. Cartesian grids with geometric adaptation are firstly generated automatically with boundary cells processed by cell-cutting and cell-merging algorithms. The nonlinear full potential equation is discretized by a finite volume scheme on these Cartesian grids and iteratively solved in an implicit fashion with a generalized minimum residual (GMRES algorithm. During computation, solution-based mesh adaptation is also applied so as to capture flow features more accurately. An improved ghost-cell method is proposed to implement the non-penetration wall boundary condition where the velocity-potential of a ghost cell is modified by an analytic method instead. According to the characteristics of the Cartesian grids, the Kutta condition is applied by specially computing the gradients on Kutta-faces without directly assigning the potential jump to cells adjacent wake faces, which can significantly improve the solution converging speed. The feasibility and accuracy of the proposed method are validated by several typical cases of sub/transonic flows around an ONERA M6 wing, a DLR-F4 wing-body, and an unconventional figuration of a blended wing body (BWB. The validation cases demonstrate a fast convergence with fully automatic grid treatment and computation, and the results suggest its capacity in application for aircraft conceptual design.

This paper describes a telescopic solver for two dimensional h adaptive grids with point singularities. The input for the telescopic solver is an h refined two dimensional computational mesh with rectangular finite elements. The candidates for point singularities are first localized over the mesh by using a greedy algorithm. Having the candidates for point singularities, we execute either a direct solver, that performs multiple refinements towards selected point singularities and executes a parallel direct solver algorithm which has logarithmic cost with respect to refinement level. The direct solvers executed over each candidate for point singularity return local Schur complement matrices that can be merged together and submitted to iterative solver. In this paper we utilize a parallel multi-thread GALOIS solver as a direct solver. We use Incomplete LU Preconditioned Conjugated Gradients (ILUPCG) as an iterative solver. We also show that elimination of point singularities from the refined mesh reduces significantly the number of iterations to be performed by the ILUPCG iterative solver.

The special importance of L1/2 regularization has been recognized in recent studies on sparse modeling (particularly on compressed sensing). The L1/2 regularization, however, leads to a nonconvex, nonsmooth, and non-Lipschitz optimization problem that is difficult to solve fast and efficiently. In this paper, through developing a threshoding representation theory for L1/2 regularization, we propose an iterative half thresholding algorithm for fast solution of L1/2 regularization, corresponding to the well-known iterative soft thresholding algorithm for L1 regularization, and the iterative hard thresholding algorithm for L0 regularization. We prove the existence of the resolvent of gradient of ||x||1/2(1/2), calculate its analytic expression, and establish an alternative feature theorem on solutions of L1/2 regularization, based on which a thresholding representation of solutions of L1/2 regularization is derived and an optimal regularization parameter setting rule is formulated. The developed theory provides a successful practice of extension of the well- known Moreau's proximity forward-backward splitting theory to the L1/2 regularization case. We verify the convergence of the iterative half thresholding algorithm and provide a series of experiments to assess performance of the algorithm. The experiments show that the half algorithm is effective, efficient, and can be accepted as a fastsolver for L1/2 regularization. With the new algorithm, we conduct a phase diagram study to further demonstrate the superiority of L1/2 regularization over L1 regularization.

We present a novel high order multiresolution Poissonsolver based on regularized Green's function solutions to obtain exact free-space boundary conditions while using fast Fourier transforms for computational efficiency. Multiresolution is a achieved through local refinement patches and regulari......We present a novel high order multiresolution Poissonsolver based on regularized Green's function solutions to obtain exact free-space boundary conditions while using fast Fourier transforms for computational efficiency. Multiresolution is a achieved through local refinement patches...... and regularized Green's functions corresponding to the difference in the spatial resolution between the patches. The full solution is obtained utilizing the linearity of the Poisson equation enabling super-position of solutions. We show that the multiresolution Poissonsolver produces convergence rates...... that correspond to the regularization order of the derived Green's functions....

We present a Newton-Krylov based solver to efficiently spin up tracers in an online ocean model. We demonstrate that the solver converges, that tracer simulations initialized with the solution from the solver have small drift, and that the solver takes orders of magnitude less computational time than the brute force spin-up approach. To demonstrate the application of the solver, we use it to efficiently spin up the tracer ideal age with respect to the circulation from different time intervals in a long physics run. We then evaluate how the spun-up ideal age tracer depends on the duration of the physics run, i.e., on how equilibrated the circulation is.

This paper presents the non-homogeneous Poisson process (NHPP) for modeling the rate of fast radio bursts (FRBs) and other infrequently observed astronomical events. The NHPP, well-known in statistics, can model changes in the rate as a function of both astronomical features and the details of an observing campaign. This is particularly helpful for rare events like FRBs because the NHPP can combine information across surveys, making the most of all available information. The goal of the paper is two-fold. First, it is intended to be a tutorial on the use of the NHPP. Second, we build an NHPP model that incorporates beam patterns and a power law flux distribution for the rate of FRBs. Using information from 12 surveys including 15 detections, we find an all-sky FRB rate of 586.88 events per sky per day above a flux of 1 Jy (95\\% CI: 271.86, 923.72) and a flux power-law index of 0.91 (95\\% CI: 0.57, 1.25). Our rate is lower than other published rates, but consistent with the rate given in Champion et al. 2016.

基于Trilinos程序包中的AztecOO和ML package开发了并行Poisson求解器。在非均匀的结构化网格上实现了复杂金属/电介质几何体的建模。 Poisson方程通过有限体积方法离散形成求解矩阵，然后利用Trilinos进行并行矩阵求解。并行测试表明，求解器的收敛表现良好，在典型情况下性能满足需求。这一求解器代码可以用于从等离子体模拟到传热过程等多种任务。%A PoissonSolver based on AztecOO and ML in Trilinos is developed. The metal and dielectric ob-ject with complex geometry is modeled in a non-uniform structure grid. Poisson equation is discretized by finite volume method to build a sparse matrix. The sparse matrix is solved paralleled with Trilinos. The benchmark show good convergence rates and satisfying performance. This solver code can be used for kinds of problem as plasma simulating and heat transfer.

Electrical impedance tomography (EIT) is a noninvasive imaging modality, where imperceptible currents are applied to the skin and the resulting surface voltages are measured. It has the potential to distinguish between ischaemic and haemorrhagic stroke with a portable and inexpensive device. The image reconstruction relies on an accurate forward model of the experimental setup. Because of the relatively small signal in stroke EIT, the finite-element modeling requires meshes of more than 10 million elements. To study the requirements in the forward modeling in EIT and also to reduce the time for experimental image acquisition, it is necessary to reduce the run time of the forward computation. We show the implementation of a parallel forward solver for EIT using the Dune-Fem C++ library and demonstrate its performance on many CPU's of a computer cluster. For a typical EIT application a direct solver was significantly slower and not an alternative to iterative solvers with multigrid preconditioning. With this new solver, we can compute the forward solutions and the Jacobian matrix of a typical EIT application with 30 electrodes on a 15-million element mesh in less than 15 min. This makes it a valuable tool for simulation studies and EIT applications with high precision requirements. It is freely available for download.

This paper presents a structural optimisation method in three-dimensional acoustic-elastic coupled problems. The proposed optimisation method finds an optimal allocation of elastic materials which reduces the sound level on some fixed observation points. In the process of the optimisation, configuration of the elastic materials is expressed with a level set function, and the distribution of the level set function is iteratively updated with the help of the topological derivative. The topological derivative is associated with state and adjoint variables which are the solutions of the acoustic-elastic coupled problems. In this paper, the acoustic-elastic coupled problems are solved by a BEM-FEM coupled solver, in which the fast multipole method (FMM) and a multi-frontal solver for sparse matrices are efficiently combined. Along with the detailed formulations for the topological derivative and the BEM-FEM coupled solver, we present some numerical examples of optimal designs of elastic sound scatterer to manipulate sound waves, from which we confirm the effectiveness of the present method.

BeamDyn, a Legendre-spectral-finite-element implementation of geometrically exact beam theory (GEBT), was developed to meet the design challenges associated with highly flexible composite wind turbine blades. In this paper, the governing equations of GEBT are reformulated into a nonlinear state-space form to support its coupling within the modular framework of the FAST wind turbine computer-aided engineering (CAE) tool. Different time integration schemes (implicit and explicit) were implemented and examined for wind turbine analysis. Numerical examples are presented to demonstrate the capability of this new beam solver. An example analysis of a realistic wind turbine blade, the CX-100, is also presented as validation.

Harmonic functions are the critical points of a Dirichlet energy functional, the linear projections of conformal maps. They play an important role in computer graphics, particularly for gradient-domain image processing and shape-preserving geometric computation. We propose Poisson coordinates, a novel transfinite interpolation scheme based on the Poisson integral formula, as a rapid way to estimate a harmonic function on a certain domain with desired boundary values. Poisson coordinates are an extension of the Mean Value coordinates (MVCs) which inherit their linear precision, smoothness, and kernel positivity. We give explicit formulas for Poisson coordinates in both continuous and 2D discrete forms. Superior to MVCs, Poisson coordinates are proved to be pseudoharmonic (i.e., they reproduce harmonic functions on n-dimensional balls). Our experimental results show that Poisson coordinates have lower Dirichlet energies than MVCs on a number of typical 2D domains (particularly convex domains). As well as presenting a formula, our approach provides useful insights for further studies on coordinates-based interpolation and fast estimation of harmonic functions.

Due to the recent explosion of interest in studying the electromagnetic behavior of large (truncated) periodic structures such as phased arrays, frequency-selective surfaces, and metamaterials, there has been a renewed interest in efficiently modeling such structures. Since straightforward numerical analyses of large, finite structures (i.e., explicitly meshing and computing interactions between all mesh elements of the entire structure) involve significant memory storage and computation times, much effort is currently being expended on developing techniques that minimize the high demand on computer resources. One such technique that belongs to the class of fastsolvers for large periodic structures is the GIFFT algorithm (Green's function interpolation and FFT), which is first discussed in [1]. This method is a modification of the adaptive integral method (AIM) [2], a technique based on the projection of subdomain basis functions onto a rectangular grid. Like the methods presented in [3]-[4], the GIFFT algorithm is an extension of the AIM method in that it uses basis-function projections onto a rectangular grid through Lagrange interpolating polynomials. The use of a rectangular grid results in a matrix-vector product that is convolutional in form and can thus be evaluated using FFTs. Although our method differs from [3]-[6] in various respects, the primary differences between the AIM approach [2] and the GIFFT method [1] is the latter's use of interpolation to represent the Green's function (GF) and its specialization to periodic structures by taking into account the reusability properties of matrices that arise from interactions between identical cell elements. The present work extends the GIFFT algorithm to allow for a complete numerical analysis of a periodic structure excited by dipole source, as shown in Fig 1. Although GIFFT [1] was originally developed to handle strictly periodic structures, the technique has now been extended to efficiently

We propose the use of highly continuous finite element spaces interconnected with low continuity hyperplanes to maximize the performance of direct solvers. Starting from a highly continuous Isogeometric Analysis (IGA) discretization, we introduce . C0-separators to reduce the interconnection between degrees of freedom in the mesh. By doing so, both the solution time and best approximation errors are simultaneously improved. We call the resulting method

The elliptic Monge-Amp\\`ere equation is a fully nonlinear Partial Differential Equation which originated in geometric surface theory, and has been applied in dynamic meteorology, elasticity, geometric optics, image processing and image registration. Solutions can be singular, in which case standard numerical approaches fail. In this article we build a finite difference solver for the Monge-Amp\\'ere equation, which converges even for singular solutions. Regularity results are used to select a priori between a stable, provably convergent monotone discretization and an accurate finite difference discretization in different regions of the computational domain. This allows singular solutions to be computed using a stable method, and regular solutions to be computed more accurately. The resulting nonlinear equations are then solved by Newton's method. Computational results in two and three dimensions validate the claims of accuracy and solution speed. A computational example is presented which demonstrates the nece...

As part of its activity, EDF R and D is developing a new nuclear core simulation code named COCAGNE. This code relies on DIABOLO, a Simplified PN (SPN) method to compute the neutron flux inside the core for eigenvalue calculations. In order to assess the accuracy of SPN calculations, we have developed DOMINO, a new 3D Cartesian SN solver. The parallel implementation of DOMINO is very efficient and allows to complete an eigenvalue calculation involving around 300 x 10{sup 9} degrees of freedom within a few hours on a single shared-memory supercomputing node. This computation corresponds to a 26-group S{sub 8} 3D PWR core model used to assess the SPN accuracy. At the pin level, the maximal error for the SP{sub 5} DIABOLO fission production rate is lower than 0.2% compared to the S{sub 8} DOMINO reference for this 3D PWR core model. (authors)

Laplacian matrices of graphs arise in large-scale computational applications such as machine learning; spectral clustering of images, genetic data and web pages; transportation network flows; electrical resistor circuits; and elliptic partial differential equations discretized on unstructured grids with finite elements. A Lean Algebraic Multigrid (LAMG) solver of the symmetric linear system Ax=b is presented, where A is a graph Laplacian. LAMG's run time and storage are linear in the number of graph edges. It is robust and requires no fine tuning. LAMG consists of a setup phase, in which a sequence of increasingly-coarser Laplacian systems is constructed, and an iterative solve phase using multigrid cycles. General graphs pose algorithmic challenges not encountered in traditional applications of algebraic multigrid. LAMG combines a lean piecewise-constant interpolation, judicious node aggregation based on a new node proximity definition, and a novel energy correction of the coarse-level systems. This results ...

In this paper the interface between the beam tracing code TORBEAM [Poli, Peeters and Pereverzev, Comp. Phys. Comm. 136, 90 (2001)] and the quasi-linear Fokker-Planck solver RELAX [Westerhof, Peeters and Schippers, Rijnhuizen Report No. RR 92-211 CA, 1992] is presented together with preliminary testing results for electron cyclotron waves in ITER plasmas and their effects on the electron distribution function. The resulting numerical package allows us to account for diffraction effects in the construction of the quasi-linear wave-particle diffusion operator. The coupling of the paraxial-WKB code TORBEAM to the ray-based code RELAX requires a reinterpretation of the paraxial wave field in terms of extended rays, which are addressed in details.

A straightforward numerical analysis of large arrays of arbitrary contour (and possibly missing elements) requires large memory storage and long computation times. Several techniques are currently under development to reduce this cost. One such technique is the GIFFT (Green's function interpolation and FFT) method discussed here that belongs to the class of fastsolvers for large structures. This method uses a modification of the standard AIM approach [1] that takes into account the reusability properties of matrices that arise from identical array elements. If the array consists of planar conducting bodies, the array elements are meshed using standard subdomain basis functions, such as the RWG basis. The Green's function is then projected onto a sparse regular grid of separable interpolating polynomials. This grid can then be used in a 2D or 3D FFT to accelerate the matrix-vector product used in an iterative solver [2]. The method has been proven to greatly reduce solve time by speeding up the matrix-vector product computation. The GIFFT approach also reduces fill time and memory requirements, since only the near element interactions need to be calculated exactly. The present work extends GIFFT to layered material Green's functions and multiregion interactions via slots in ground planes. In addition, a preconditioner is implemented to greatly reduce the number of iterations required for a solution. The general scheme of the GIFFT method is reported in [2]; this contribution is limited to presenting new results for array antennas made of slot-excited patches and cavity-backed patch antennas.

We define the class of sequentially semi-separable matrices in this paper. Essentially this is the class of matrices which have low numerical rank on their off diagonal blocks. Examples include banded matrices, semi-separable matrices, their sums as well as inverses of these sums. Fast and stable algorithms for solving linear systems of equations involving such matrices and computing Moore-Penrose inverses are presented. Supporting numerical results are also presented. In addition, fast algorithms to construct and update this matrix structure for any given matrix are presented. Finally, numerical results that show that the coefficient matrices resulting from global spectral discretizations of certain integral equations indeed have this matrix structure are given.

In many cities, ambient air quality is deteriorating leading to concerns about the health of city inhabitants. In urban areas with narrow streets surrounded by clusters of tall buildings, called street canyons, air pollution from traffic emissions and other sources is difficult to disperse and may accumulate resulting in high pollutant concentrations. For various situations, including the evacuation of populated areas in the event of an accidental or deliberate release of chemical, biological and radiological agents, it is important that models should be developed that produce urban flow fields quickly. For these reasons it has become important to predict the flow field in urban street canyons. Various computational techniques have been used to calculate these flow fields, but these techniques are often computationally intensive. Most fast response models currently in use are at a disadvantage in these cases as they are unable to correlate highly heterogeneous urban structures with the diagnostic parameterizations on which they are based. In this paper, a fast and reasonably accurate computational fluid dynamics (CFD) technique that solves the Navier-Stokes equations for complex urban areas has been developed called QUIC-CFD (Q-CFD). This technique represents an intermediate balance between fast (on the order of minutes for a several block problem) and reasonably accurate solutions. The paper details the solution procedure and validates this model for various simple and complex urban geometries.

The Monte-Carlo method is often presented as a reference method for radiative transfer simulation when dealing with participating, inhomogeneous media. The reason is that numerical uncertainties are only of a statistical nature and are accurately evaluated by measuring the standard deviation of the Monte Carlo weight. But classical Monte-Carlo algorithms first sample optical thicknesses and then determine absorption or scattering locations by inverting the formal integral definition of optical thickness as an increasing function of path length. This function is only seldom analytically invertible and numerical inversion procedures are required. Most commonly, a volumic grid is introduced and optical properties within each cell are replaced by approximate homogeneous or linear fields. Simulation results are then sensitive to the grid and can no longer be considered as references. We propose a new algorithmic formulation based on the use of null-collisions that eliminate the need for numerical inversion: no volumic grid is required. Benchmark configurations are first considered in order to evaluate the effect of two free parameters: the amount of null-collisions, and the criterion used to decide at which stage a Russian Roulette is used to exit the path tracking process. Then the corresponding algorithm is implemented using a development environment allowing to deal with complex geometries (thanks to computer graphics techniques), leading to a Monte Carlo code that can be easily used for validation of fast radiative transfer solvers embedded in combustion simulators. "Easily" means here that the way the Monte Carlo algorithm deals with both the geometry and the temperature/pressure/concentration fields is independent of the choices made inside the combustion solver: there is no need for the design of a new path-tracking procedure adapted to each new CFD grid. The Monte Carlo simulator is ready for use as soon as combustion specialists provide a localization

A fast sweeping method (FSM) determines the first arrival traveltimes of seismic waves by sweeping the velocity model in different directions meanwhile applying a local solver. It is an efficient way to numerically solve Hamilton-Jacobi equations for traveltime calculations. In this study, we develop an improved FSM to calculate the first arrival traveltimes of quasi-P (qP) waves in 2-D tilted transversely isotropic (TTI) media. A local solver utilizes the coupled slowness surface of qP and quasi-SV (qSV) waves to form a quartic equation, and solve it numerically to obtain possible traveltimes of qP-wave. The proposed quartic solver utilizes Fermat's principle to limit the range of the possible solution, then uses the bisection procedure to efficiently determine the real roots. With causality enforced during sweepings, our FSM converges fast in a few iterations, and the exact number depending on the complexity of the velocity model. To improve the accuracy, we employ high-order finite difference schemes and derive the second-order formulae. There is no weak anisotropy assumption, and no approximation is made to the complex slowness surface of qP-wave. In comparison to the traveltimes calculated by a horizontal slowness shooting method, the validity and accuracy of our FSM is demonstrated.

This paper considers geometric ergodicity and likelihood based inference for linear and nonlinear Poisson autoregressions. In the linear case the conditional mean is linked linearly to its past values as well as the observed values of the Poisson process. This also applies to the conditional...

This paper considers geometric ergodicity and likelihood based inference for linear and nonlinear Poisson autoregressions. In the linear case the conditional mean is linked linearly to its past values as well as the observed values of the Poisson process. This also applies to the conditional...... variance, implying an interpretation as an integer valued GARCH process. In a nonlinear conditional Poisson model, the conditional mean is a nonlinear function of its past values and a nonlinear function of past observations. As a particular example an exponential autoregressive Poisson model for time...... series is considered. Under geometric ergodicity the maximum likelihood estimators of the parameters are shown to be asymptotically Gaussian in the linear model. In addition we provide a consistent estimator of the asymptotic covariance, which is used in the simulations and the analysis of some...

In this article we consider geometric ergodicity and likelihood-based inference for linear and nonlinear Poisson autoregression. In the linear case, the conditional mean is linked linearly to its past values, as well as to the observed values of the Poisson process. This also applies...... to the conditional variance, making possible interpretation as an integer-valued generalized autoregressive conditional heteroscedasticity process. In a nonlinear conditional Poisson model, the conditional mean is a nonlinear function of its past values and past observations. As a particular example, we consider...... an exponential autoregressive Poisson model for time series. Under geometric ergodicity, the maximum likelihood estimators are shown to be asymptotically Gaussian in the linear model. In addition, we provide a consistent estimator of their asymptotic covariance matrix. Our approach to verifying geometric...

This paper considers geometric ergodicity and likelihood based inference for linear and nonlinear Poisson autoregressions. In the linear case the conditional mean is linked linearly to its past values as well as the observed values of the Poisson process. This also applies to the conditional...... variance, making an interpretation as an integer valued GARCH process possible. In a nonlinear conditional Poisson model, the conditional mean is a nonlinear function of its past values and a nonlinear function of past observations. As a particular example an exponential autoregressive Poisson model...... for time series is considered. Under geometric ergodicity the maximum likelihood estimators of the parameters are shown to be asymptotically Gaussian in the linear model. In addition we provide a consistent estimator of their asymptotic covariance matrix. Our approach to verifying geometric ergodicity...

A new original code for solving the 3-D relativistic and bounce-averaged electron drift kinetic equation is presented. It designed for the current drive problem in tokamak with an arbitrary magnetic equilibrium. This tool allows self-consistent calculations of the bootstrap current in presence of other external current sources. RF current drive for arbitrary type of waves may be used. Several moments of the electron distribution function are determined, like the exact and effective fractions of trapped electrons, the plasma current, absorbed RF power, runaway and magnetic ripple loss rates and non-thermal Bremsstrahlung. Advanced numerical techniques have been used to make it the first fully implicit (reverse time) 3-D solver, particularly well designed for implementation in a chain of code for realistic current drive calculations in high {beta}{sub p} plasmas. All the details of the physics background and the numerical scheme are presented, as well a some examples to illustrate main code capabilities. Several important numerical points are addressed concerning code stability and potential numerical and physical limitations. (authors)

We consider the problem of estimating parameters in large-scale weakly nonlinear inverse problems for which the underlying governing equations is a linear, time-dependent, parabolic partial differential equation. A major challenge in solving these inverse problems using Newton-type methods is the computational cost associated with solving the forward problem and with repeated construction of the Jacobian, which represents the sensitivity of the measurements to the unknown parameters. Forming the Jacobian can be prohibitively expensive because it requires repeated solutions of the forward and adjoint time-dependent parabolic partial differential equations corresponding to multiple sources and receivers. We propose an efficient method based on a Laplace transform-based exponential time integrator combined with a flexible Krylov subspace approach to solve the resulting shifted systems of equations efficiently. Our proposed solver speeds up the computation of the forward and adjoint problems, thus yielding significant speedup in total inversion time. We consider an application from Transient Hydraulic Tomography (THT), which is an imaging technique to estimate hydraulic parameters related to the subsurface from pressure measurements obtained by a series of pumping tests. The algorithms discussed are applied to a synthetic example taken from THT to demonstrate the resulting computational gains of this proposed method.

Full Text Available The atmospheric chemistry general circulation model ECHAM5/MESSy (EMAC and the atmospheric chemistry box model CAABA are extended by a computationally very efficient submodel for atmospheric chemistry, E4CHEM. It focuses on stratospheric chemistry but also includes background tropospheric chemistry. It is based on the chemistry of MAECHAM4-CHEM and is intended to serve as a simple and fast alternative to the flexible but also computationally more demanding submodel MECCA. In a model setup with E4CHEM, EMAC is now also suitable for simulations of longer time scales. The reaction mechanism contains basic O3, CH4, CO, HOx, NOx and ClOx gas phase chemistry. In addition, E4CHEM includes optional fast routines for heterogeneous reactions on sulphate aerosols and polar stratospheric clouds (substituting the existing submodels PSC and HETCHEM, and scavenging (substituting the existing submodel SCAV. We describe the implementation of E4CHEM into the MESSy structure of CAABA and EMAC. For some species the steady state in the box model differs by up to 100% when compared to results from CAABA/MECCA due to different reaction rates. After an update of the reaction rates in E4CHEM the mixing ratios in both boxmodel and 3-D model simulations are in satisfactory agreement with the results from a simulation where MECCA with a similar chemistry scheme was employed. Finally, a comparison against a simulation with a more complex and already evaluated chemical mechanism is presented in order to discuss shortcomings associated with the simplification of the chemical mechanism.

For the solution of the time-harmonic electromagnetic scattering problem by inhomogeneous 3-D objects, a one-way domain decomposition method (DDM) is considered: the computational domain is partitioned into concentric subdomains on the interfaces of which Robin-type transmission conditions (TCs) are prescribed; an integral representation of the electromagnetic fields on the outer boundary constitutes an exact radiation condition. The global system obtained after discretization of the finite element (FE) formulations is solved via a Krylov subspace iterative method (GMRES). It is preconditioned in such a way that, essentially, only the solution of the FE subsystems in each subdomain is required. This is made possible by a computationally cheap H (curl)- H (div) transformation performed on the interfaces that separate the two outermost subdomains. The eigenvalues of the preconditioned matrix of the system are bounded by two, and optimized values of the coefficients involved in the local TCs on the interfaces are determined so as to maximize the minimum eigenvalue. Numerical experiments are presented that illustrate the numerical accuracy of this technique, its fast convergence, and legitimate the choices made for the optimized coefficients.

Composing constraint solvers based on tree search and constraint propagation through generic iteration leads to efficient and flexible constraint solvers. This was demonstrated using OpenSolver, an abstract branch-and-propagate tree search engine that supports a wide range of relevant solver configu

This report describes the numerical procedure used to implement the Green`s function method for solving the Poisson equation in two-dimensional (r,z) cylindrical coordinates. The procedure can determine the solution to a problem with any or all of the applied voltage boundary conditions, dielectric media, floating (insulated) conducting media, dielectric surface charging, and volumetric space charge. The numerical solution is reasonably fast, and the dimension of the linear problem to be solved is that of the number of elements needed to represent the surfaces, not the whole computational volume. The method of solution is useful in the simulation of plasma particle motion in the vicinity of complex surface structures as found in microelectronics plasma processing applications. This report is a stand-alone supplement to the previous Sandia Technical Report SAND98-0537 presenting the two-dimensional Cartesian Poissonsolver.

This edited volume offers a state of the art overview of fast and robust solvers for the Helmholtz equation. The book consists of three parts: new developments and analysis in Helmholtz solvers, practical methods and implementations of Helmholtz solvers, and industrial applications. The Helmholtz equation appears in a wide range of science and engineering disciplines in which wave propagation is modeled. Examples are: seismic inversion, ultrasone medical imaging, sonar detection of submarines, waves in harbours and many more. The partial differential equation looks simple but is hard to solve. In order to approximate the solution of the problem numerical methods are needed. First a discretization is done. Various methods can be used: (high order) Finite Difference Method, Finite Element Method, Discontinuous Galerkin Method and Boundary Element Method. The resulting linear system is large, where the size of the problem increases with increasing frequency. Due to higher frequencies the seismic images need to b...

Poisson algebras are fundamental algebraic structures in physics and symplectic geometry. However, the structure theory of Poisson algebras has not been well developed. In this paper, we determine the structure of the central simple Poisson algebras related to locally finite derivations, over an algebraically closed field of characteristic zero.The Lie algebra structures of these Poisson algebras are in general not finitely-graded.

REA's Problem Solvers is a series of useful, practical, and informative study guides. Each title in the series is complete step-by-step solution guide. The Differential Equations Problem Solver enables students to solve difficult problems by showing them step-by-step solutions to Differential Equations problems. The Problem Solvers cover material ranging from the elementary to the advanced and make excellent review books and textbook companions. They're perfect for undergraduate and graduate studies.The Differential Equations Problem Solver is the perfect resource for any class, any exam, and

We establish the concept of a quotient affine Poisson group, and study the reduced Poisson action of the quotient of an affine Poisson group G on the quotient of an affine Poisson G-variety V. The Poisson morphisms (including equivariant cases) between Poisson affine varieties are also discussed.

We propose an efficient algorithm for the evaluation of the potential and its gradient of gravitational/electrostatic $N$-body systems, which we call particle mesh multipole method (PMMM or PM$^3$). PMMM can be understood both as an extension of the particle mesh (PM) method and as an optimization of the fast multipole method (FMM).In the former viewpoint, the scalar density and potential held by a grid point are extended to multipole moments and local expansions in $(p+1)^2$ real numbers, where $p$ is the order of expansion. In the latter viewpoint, a hierarchical octree structure which brings its $\\mathcal O(N)$ nature, is replaced with a uniform mesh structure, and we exploit the convolution theorem with fast Fourier transform (FFT) to speed up the calculations. Hence, independent $(p+1)^2$ FFTs with the size equal to the number of grid points are performed. The fundamental idea is common to PPPM/MPE by Shimada et al. (1993) and FFTM by Ong et al. (2003). PMMM differs from them in supporting both the open ...

Full Text Available A new mixture of Modified Exponential (ME and Poisson distribution has been introduced in this paper. Taking the Maximum of Modified Exponential random variable when the sample size follows a zero truncated Poisson distribution we have derived the new distribution, named as Extended Poisson Exponential distribution. This distribution possesses increasing and decreasing failure rates. The Poisson-Exponential, Modified Exponential and Exponential distributions are special cases of this distribution. We have also investigated some mathematical properties of the distribution along with Information entropies and Order statistics of the distribution. The estimation of parameters has been obtained using the Maximum Likelihood Estimation procedure. Finally we have illustrated a real data application of our distribution.

To extract parasitic capacitances in wiring structures of integrated circuits the authors developed the two- and three-dimensional finite element program SCAP (Smart Capacitance Analysis Program). The program computes the task of the electrostatic field from a solution of Poisson`s equation via finite elements and calculates the energies from which the capacitance matrix is extracted. The unknown potential vector, which has for three-dimensional applications 5000-50000 unknowns, is computed by a ICCG solver. Currently three- and six-node triangular, four- and ten-node tetrahedronal elements are supported.

We present an algorithm which allows a fast numerical computation of Feldman-Cousins confidence intervals for Poisson processes, even when the number of background events is relatively large. This algorithm incorporates an appropriate treatment of the singularities that arise as a consequence of the discreteness of the variable.

We present an algorithm which allows a fast numerical computation of Feldman-Cousins confidence intervals for Poisson processes, even when the number of background events is relatively large. This algorithm incorporates an appropriate treatment of the singularities that arise as a consequence of the discreteness of the variable.

What constitutes jointly Poisson processes remains an unresolved issue. This report reviews the current state of the theory and indicates how the accepted but unproven model equals that resulting from the small time-interval limit of jointly Bernoulli processes. One intriguing consequence of these models is that jointly Poisson processes can only be positively correlated as measured by the correlation coefficient defined by cumulants of the probability generating functional.

We present a new, robust and fast, three-dimensional (3-D) magnetotelluric (MT) inverse solver. As a forward modelling engine a highly-scalable solver extrEMe [1] is used. The (regularized) inversion is based on an iterative gradient-type optimization (quasi-Newton method) and exploits adjoint sources approach for fast calculation of the gradient of the misfit. The inverse solver is able to deal with highly detailed and contrasting models, allows for working (separately or jointly) with any type of MT (single-site and/or inter-site) responses, and supports massive parallelization. Different parallelization strategies implemented in the code allow for optimal usage of available computational resources for a given problem set up. To parameterize an inverse domain a mask approach is implemented, which means that one can merge any subset of forward modelling cells in order to account for (usually) irregular distribution of observation sites. We report results of 3-D numerical experiments aimed at analysing the robustness, performance and scalability of the code. In particular, our computational experiments carried out at different platforms ranging from modern laptops to high-performance clusters demonstrate practically linear scalability of the code up to thousands of nodes. 1. Kruglyakov, M., A. Geraskin, A. Kuvshinov, 2016. Novel accurate and scalable 3-D MT forward solver based on a contracting integral equation method, Computers and Geosciences, in press.

Sets of tridiagonal systems occur in many applications. FastPoissonsolvers and Alternate Direction Methods make use of tridiagonal system solvers. Network-based multiprocessors provide a cost-effective alternative to traditional supercomputer architectures. The complexity of concurrent algorithms for the solution of multiple tridiagonal systems on Boolean-cube-configured multiprocessors with distributed memory are investigated. Variations of odd-even cyclic reduction, parallel cyclic reduction, and algorithms making use of data transposition with or without substructuring and local elimination, or pipelined elimination, are considered. A simple performance model is used for algorithm comparison, and the validity of the model is verified on an Intel iPSC/1. For many combinations of machine and system parameters, pipelined elimination, or equation transposition with or without substructuring is optimum. Hybrid algorithms that at any stage choose the best algorithm among the considered ones for the remainder of the problem are presented. It is shown that the optimum partitioning of a set of independent tridiagonal systems among a set of processors yields the embarrassingly parallel case.

time of the solver and the aim of this note is to provide some insight into which formulations are better than others. The experiments addresses three general issues: (i) the order of the parameters of relations, (ii) the order of conjuncts in preconditions and (iii) the use of memoisation....... The experiments are performed for Control Flow Analyses for Discretionary Ambients....

In this paper, we report results of the performance, convergence, and accuracy of a parallel GMRES solver for Boundary Element Methods. The solver uses a hierarchical approximate matrix-vector product based on a hybrid Barnes-Hut / Fast Multipole Method. We study the impact of various accuracy parameters on the convergence and show that with minimal loss in accuracy, our solver yields significant speedups. We demonstrate the excellent parallel efficiency and scalability of our solver. The combined speedups from approximation and parallelism represent an improvement of several orders in solution time. We also develop fast and paralellizable preconditioners for this problem. We report on the performance of an inner-outer scheme and a preconditioner based on truncated Green`s function. Experimental results on a 256 processor Cray T3D are presented.

We develop a frequency-domain iterative solver for numerical simulation of acoustic waves in 3D heterogeneous media. It is based on the application of a unique preconditioner to the Helmholtz equation that ensures convergence for Krylov subspace iteration methods. Effective inversion of the preconditioner involves the Fast Fourier Transform (FFT) and numerical solution of a series of boundary value problems for ordinary differential equations. Matrix-by-vector multiplication for iterative inversion of the preconditioned matrix involves inversion of the preconditioner and pointwise multiplication of grid functions. Our solver has been verified by benchmarking against exact solutions and a time-domain solver.

A general master action in terms of superfields is given which generates generalized Poisson sigma models by means of a natural ghost number prescription. The simplest representation is the sigma model considered by Cattaneo and Felder. For Dirac brackets considerably more general models are generated.

We investigate the counting statistics for stationary and nonstationary cascaded Poisson processes. A simple equation is obtained for the variance-to-mean ratio in the limit of long counting times. Explicit expressions for the forward-recurrence and inter-event-time probability density functions are also obtained. The results are expected to be of use in a number of areas of physics.

Poisson have been proposed. Atkinson [5] includes the approach developed in Marsaglia £15) and Norman and Cannon £16) which is based on composition...34, Naval Research Logistics Quarterly, 26, 3, 403-413. 15. Marsaglia , G. (1963). "Generating Discrete Random Variables in a Computer", Communications

The formulation of optimal control problems governed by Fredholm integral equations of second kind and an efficient computational framework for solving these control problems is presented. Existence and uniqueness of optimal solutions is proved.A collective Gauss-Seidel scheme and a multigrid scheme are discussed. Optimal computational performance of these iterative schemes is proved by local Fourier analysis and demonstrated by results of numerical experiments.

A lattice Boltzmann formulation for relativistic fluids is presented and numerically validated through quantitative comparison with recent hydrodynamic simulations of relativistic fluids. In order to illustrate its capability to handle complex geometries, the scheme is also applied to the case of a three-dimensional relativistic shock wave, generated by a supernova explosion, impacting on a massive interstellar cloud. This formulation opens up the possibility of exporting the proven advantages of lattice Boltzmann methods, namely, computational efficiency and easy handling of complex geometries, to the context of (mildly) relativistic fluid dynamics at large, from quark-gluon plasmas up to supernovae with relativistic outflows.

Developing accurate solvers for the Poisson Boltzmann (PB) model is the first step to make the PB model suitable for implicit solvent simulation. Reducing the grid size influence on the performance of the solver benefits to increasing the speed of solver and providing accurate electrostatics analysis for solvated molecules. In this work, we explore the accurate coarse grid PB solver based on the Green's function treatment of the singular charges, matched interface and boundary (MIB) method for treating the geometric singularities, and posterior electrostatic potential field extension for calculating the reaction field energy. We made our previous PB software, MIBPB, robust and provides almost grid size independent reaction field energy calculation. Large amount of the numerical tests verify the grid size independence merit of the MIBPB software. The advantage of MIBPB software directly make the acceleration of the PB solver from the numerical algorithm instead of utilization of advanced computer architectures...

Let (M,π) be a Poisson manifold. A Poisson submanifold P ⊂ M gives rise to a Lie algebroid AP → P. Formal deformations of π around P are controlled by certain cohomology groups associated to AP. Assuming that these groups vanish, we prove that π is formally rigid around P; that is, any other Poisson

We introduce a new collection of solvers - subsequently called EleMRRR - for large-scale dense Hermitian eigenproblems. EleMRRR solves various types of problems: generalized, standard, and tridiagonal eigenproblems. Among these, the last is of particular importance as it is a solver on its own right, as well as the computational kernel for the first two; we present a fast and scalable tridiagonal solver based on the Algorithm of Multiple Relatively Robust Representations - referred to as PMRRR. Like the other EleMRRR solvers, PMRRR is part of the freely available Elemental library, and is designed to fully support both message-passing (MPI) and multithreading parallelism (SMP). As a result, the solvers can equally be used in pure MPI or in hybrid MPI-SMP fashion. We conducted a thorough performance study of EleMRRR and ScaLAPACK's solvers on two supercomputers. Such a study, performed with up to 8,192 cores, provides precise guidelines to assemble the fastest solver within the ScaLAPACK framework; it also ind...

This book covers local search for combinatorial optimization and its extension to mixed-variable optimization. Although not yet understood from the theoretical point of view, local search is the paradigm of choice for tackling large-scale real-life optimization problems. Today's end-users demand interactivity with decision support systems. For optimization software, this means obtaining good-quality solutions quickly. Fast iterative improvement methods, like local search, are suited to satisfying such needs. Here the authors show local search in a new light, in particular presenting a new kind of mathematical programming solver, namely LocalSolver, based on neighborhood search. First, an iconoclast methodology is presented to design and engineer local search algorithms. The authors' concern about industrializing local search approaches is of particular interest for practitioners. This methodology is applied to solve two industrial problems with high economic stakes. Software based on local search induces ex...

Many random populations can be modeled as a countable set of points scattered randomly on the positive half-line. The points may represent magnitudes of earthquakes and tornados, masses of stars, market values of public companies, etc. In this article we explore a specific class of random such populations we coin ` Paretian Poisson processes'. This class is elemental in statistical physics—connecting together, in a deep and fundamental way, diverse issues including: the Poisson distribution of the Law of Small Numbers; Paretian tail statistics; the Fréchet distribution of Extreme Value Theory; the one-sided Lévy distribution of the Central Limit Theorem; scale-invariance, renormalization and fractality; resilience to random perturbations.

Each Problem Solver is an insightful and essential study and solution guide chock-full of clear, concise problem-solving gems. All your questions can be found in one convenient source from one of the most trusted names in reference solution guides. More useful, more practical, and more informative, these study aids are the best review books and textbook companions available. Nothing remotely as comprehensive or as helpful exists in their subject anywhere. Perfect for undergraduate and graduate studies.Here in this highly useful reference is the finest overview of electric circuits currently av

Each Problem Solver is an insightful and essential study and solution guide chock-full of clear, concise problem-solving gems. All your questions can be found in one convenient source from one of the most trusted names in reference solution guides. More useful, more practical, and more informative, these study aids are the best review books and textbook companions available. Nothing remotely as comprehensive or as helpful exists in their subject anywhere. Perfect for undergraduate and graduate studies.Here in this highly useful reference is the finest overview of advanced calculus currently av

When the Poisson matrix of Poisson system is non-constant, classical symplectic methods, such as symplectic Runge-Kutta method, generating function method, cannot preserve the Poisson structure. The non-constant Poisson structure was transformed into the symplectic structure by the nonlinear transform.Arbitrary order symplectic method was applied to the transformed Poisson system. The Euler equation of the free rigid body problem was transformed into the symplectic structure and computed by the mid-point scheme. Numerical results show the effectiveness of the nonlinear transform.

with a complementary spatial point process Y to obtain a Poisson process X∪Y with intensity function β. Underlying this is a bivariate spatial birth-death process (Xt,Yt) which converges towards the distribution of (X,Y). We study the joint distribution of X and Y, and their marginal and conditional distributions...... process with intensity function β if and only if the true Papangelou intensity is used. Whether the superposition is actually such a Poisson process can easily be examined using well known results and fast simulation procedures for Poisson processes. We illustrate this approach to model checking....... In particular, we introduce a fast and easy simulation procedure for Y conditional on X. This may be used for model checking: given a model for the Papangelou intensity of the original spatial point process, this model is used to generate the complementary process, and the resulting superposition is a Poisson...

The size-modified Poisson-Boltzmann (MPB) equation is an efficient implicit solvation model which also captures electrolytic solvent effects. It combines an account of the dielectric solvent response with a mean-field description of solvated finite-sized ions. We present a general solution scheme for the MPB equation based on a fast function-space-oriented Newton method and a Green's function preconditioned iterative linear solver. In contrast to popular multigrid solvers, this approach allows us to fully exploit specialized integration grids and optimized integration schemes. We describe a corresponding numerically efficient implementation for the full-potential density-functional theory (DFT) code FHI-aims. We show that together with an additional Stern layer correction the DFT+MPB approach can describe the mean activity coefficient of a KCl aqueous solution over a wide range of concentrations. The high sensitivity of the calculated activity coefficient on the employed ionic parameters thereby suggests to use extensively tabulated experimental activity coefficients of salt solutions for a systematic parametrization protocol.

In this paper we give an overview of the present state of fastsolvers for the solution of the incompressible Navier-Stokes equations discretized by the finite element method and linearized by Newton or Picard's method. It is shown that block precon- ditioners form an excellent approach for the solution, however if the grids are not to fine preconditioning with a Saddle point ILU matrix (SILU) may be an attractive al- ternative. The applicability of all methods to stabilized elements is investigated. In case of the stand-alone Stokes equations special preconditioners increase the efficiency considerably.

A regularisation method for solving the Poisson equation using Green’s functions is presented.The method is shown to obtain a convergence rate which corresponds to the design of the regularised Green’s function and a spectral-like convergence rate is obtained using a spectrally ideal regularisation...... the appropriate regularised Green’s functions. Using an analogy to the particle-particle particle-mesh method, a framework for calculating multi-resolution solutions using local refinement patches is presented. The regularised Poissonsolver is shown to maintain a high order converging solution for different...... configurations of the refinement patches.The regularised Poissonsolver has been implemented in a high order particle-mesh based vortex method for simulating incompressible fluid flow. A re-meshing of the vortex particlesis used to ensure the convergence of the method and a re-projection of the vorticity field...

ABSTRACT: The FAST project (Food Allergy Specific Immunotherapy) aims at the development of safe and effective treatment of food allergies, targeting prevalent, persistent and severe allergy to fish and peach. Classical allergen-specific immunotherapy (SIT), using subcutaneous injections with aqu......ABSTRACT: The FAST project (Food Allergy Specific Immunotherapy) aims at the development of safe and effective treatment of food allergies, targeting prevalent, persistent and severe allergy to fish and peach. Classical allergen-specific immunotherapy (SIT), using subcutaneous injections...... with aqueous food extracts may be effective but has proven to be accompanied by too many anaphylactic side-effects. FAST aims to develop a safe alternative by replacing food extracts with hypoallergenic recombinant major allergens as the active ingredients of SIT. Both severe fish and peach allergy are caused...... in depth serological and cellular immune analyses will be performed, allowing identification of novel biomarkers for monitoring treatment efficacy. FAST aims at improving the quality of life of food allergic patients by providing a safe and effective treatment that will significantly lower their threshold...

In this paper, we study the interplay between modules and sub-objects in holomorphic Poisson geometry. In particular, we define a new notion of "residue" for a Poisson module, analogous to the Poincar\\'e residue of a meromorphic volume form. Of particular interest is the interaction between the residues of the canonical line bundle of a Poisson manifold and its degeneracy loci---where the rank of the Poisson structure drops. As an application, we provide new evidence in favour of Bondal's conjecture that the rank \\leq 2k locus of a Fano Poisson manifold always has dimension \\geq 2k+1. In particular, we show that the conjecture holds for Fano fourfolds. We also apply our techniques to a family of Poisson structures defined by Fe\\u{\\i}gin and Odesski\\u{\\i}, where the degeneracy loci are given by the secant varieties of elliptic normal curves.

This is an overview of our accomplishments during the final term of this grant (1 September 2008 -- 30 June 2012). These fall mainly into three categories: fast algorithms for linear eigenvalue problems; solution algorithms and modeling methods for partial differential equations with uncertain coefficients; and preconditioning methods and solvers for models of computational fluid dynamics (CFD).

Due to noise considerations, ultra high bypass ducted fans have become a more viable design. These ducted fans typically consist of a rotor stage containing a wide chord fan and a stator stage. One of the concerns for this design is the classical flutter that keeps occurring in various unducted fan blade designs. These flutter are catastrophic and are to be avoided in the flight envelope of the engine. Some numerical investigations by Williams, Cho and Dalton, have suggested that a duct around a propeller makes it more unstable. This needs to be further investigated. In order to design an engine to safely perform a set of desired tasks, accurate information of the stresses on the blade during the entire cycle of blade motion is required. This requirement in turn demands that accurate knowledge of steady and unsteady blade loading be available. Aerodynamic solvers based on unsteady three-dimensional analysis will provide accurate and fast solutions and are best suited for aeroelastic analysis. The Euler solvers capture significant physics of the flowfield and are reasonably fast. An aerodynamic solver Ref. based on Euler equations had been developed under a separate grant from NASA Lewis in the past. Under the current grant, this solver has been modified to calculate the aeroelastic characteristics of unducted and ducted rotors. Even though, the aeroelastic solver based on three-dimensional Euler equations is computationally efficient, it is still very expensive to investigate the effects of multiple stages on the aeroelastic characteristics. In order to investigate the effects of multiple stages, a two-dimensional multi stage aeroelastic solver was also developed under this task, in collaboration with Dr. T. S. R. Reddy of the University of Toledo. Both of these solvers were applied to several test cases and validated against experimental data, where available.

The Central Limit Theorem (CLT) and Extreme Value Theory (EVT) study, respectively, the stochastic limit-laws of sums and maxima of sequences of independent and identically distributed (i.i.d.) random variables via an affine scaling scheme. In this research we study the stochastic limit-laws of populations of i.i.d. random variables via nonlinear scaling schemes. The stochastic population-limits obtained are fractal Poisson processes which are statistically self-similar with respect to the scaling scheme applied, and which are characterized by two elemental structures: (i) a universal power-law structure common to all limits, and independent of the scaling scheme applied; (ii) a specific structure contingent on the scaling scheme applied. The sum-projection and the maximum-projection of the population-limits obtained are generalizations of the classic CLT and EVT results - extending them from affine to general nonlinear scaling schemes.

In this paper, we propose a class of non-Gaussian stationary increment processes, named nonhomogeneous fractional Poisson processes W{sub H}{sup (j)}(t), which permit the study of the effects of long-range dependance in a large number of fields including quantum physics and finance. The processes W{sub H}{sup (j)}(t) are self-similar in a wide sense, exhibit more fatter tail than Gaussian processes, and converge to the Gaussian processes in distribution in some cases. In addition, we also show that the intensity function {lambda}(t) strongly influences the existence of the highest finite moment of W{sub H}{sup (j)}(t) and the behaviour of the tail probability of W{sub H}{sup (j)}(t)

Membrane protein systems are important computational research topics due to their roles in rational drug design. In this study, we developed a continuum membrane model utilizing a level set formulation under the numerical Poisson-Boltzmann framework within the AMBER molecular mechanics suite for applications such as protein-ligand binding affinity and docking pose predictions. Two numerical solvers were adapted for periodic systems to alleviate possible edge effects. Validation on systems ranging from organic molecules to membrane proteins up to 200 residues, demonstrated good numerical properties. This lays foundations for sophisticated models with variable dielectric treatments and second-order accurate modeling of solvation interactions.

The self-consistent modeling of vacuum polarization due to virtual electron-positron fluctuations is of relevance for many near term experiments associated with high intensity radiation sources and represents a milestone in describing scenarios of extreme energy density. We present a generalized finite-difference time-domain solver that can incorporate the modifications to Maxwells equations due to virtual vacuum polarization. Our multidimensional solver reproduced in one dimensional configurations the results for which an analytic treatment is possible, yielding vacuum harmonic generation and birefringence. The solver has also been tested for two-dimensional scenarios where finite laser beam spot sizes must be taken into account. We employ this solver to explore different types of counter-propagating configurations that can be relevant for future planned experiments aiming to detect quantum vacuum dynamics at ultra-high electromagnetic field intensities.

In this paper we describe a unique method for obtaining the famous Poisson spot without adding obstacles to the light path, which could interfere with the effect. A Poisson spot is the interference effect from parallel rays of light diffracting around a solid spherical object, creating a bright spot in the center of the shadow.

The Poisson geometry of a discrete string in three dimensional Euclidean space is investigated. For this the Frenet frames are converted into a spinorial representation, the discrete spinor Frenet equation is interpreted in terms of a transfer matrix formalism, and Poisson brackets are introduced in terms of the spinor components. The construction is then generalised, in a self-similar manner, into an infinite hierarchy of Poisson algebras. As an example, the classical Virasoro (Witt) algebra that determines reparametrisation diffeomorphism along a continuous string, is identified as a particular sub-algebra, in the hierarchy of the discrete string Poisson algebra. - Highlights: • Witt (classical Virasoro) algebra is derived in the case of discrete string. • Infinite dimensional hierarchy of Poisson bracket algebras is constructed for discrete strings. • Spinor representation of discrete Frenet equations is developed.

We present novel, robust, scalable, and fast 3-D magnetotelluric (MT) inverse solver. The solver is written in multi-language paradigm to make it as efficient, readable and maintainable as possible. Separation of concerns and single responsibility concepts go through implementation of the solver. As a forward modelling engine a modern scalable solver extrEMe, based on contracting integral equation approach, is used. Iterative gradient-type (quasi-Newton) optimization scheme is invoked to search for (regularized) inverse problem solution, and adjoint source approach is used to calculate efficiently the gradient of the misfit. The inverse solver is able to deal with highly detailed and contrasting models, allows for working (separately or jointly) with any type of MT responses, and supports massive parallelization. Moreover, different parallelization strategies implemented in the code allow optimal usage of available computational resources for a given problem statement. To parameterize an inverse domain the so-called mask parameterization is implemented, which means that one can merge any subset of forward modelling cells in order to account for (usually) irregular distribution of observation sites. We report results of 3-D numerical experiments aimed at analysing the robustness, performance and scalability of the code. In particular, our computational experiments carried out at different platforms ranging from modern laptops to HPC Piz Daint (6th supercomputer in the world) demonstrate practically linear scalability of the code up to thousands of nodes.

In this paper we introduce color Hom-Poisson algebras and show that every color Hom-associative algebra has a non-commutative Hom-Poisson algebra structure in which the Hom-Poisson bracket is the commutator bracket. Then we show that color Poisson algebras (respectively morphism of color Poisson algebras) turn to color Hom-Poisson algebras (respectively morphism of Color Hom-Poisson algebras) by twisting the color Poisson structure. Next we prove that modules over color Hom–associative algebr...

The vector field generating reversible time evolution of macroscopic systems involves two ingredients: gradient of a potential (a covector) and a degenerate Poisson structure transforming the covector into a vector. The Poisson structure is conveniently expressed in Poisson brackets, its degeneracy in their Casimirs (i.e. potentials whose gradients produce no vector field). In this paper we investigate in detail hierarchies of Poisson brackets, together with their Casimirs, that arise in passages from more to less detailed (i.e. more macroscopic) descriptions. In particular, we investigate the passage from mechanics of particles (in its Liouville representation) to the reversible kinetic theory and the passage from the reversible kinetic theory to the reversible fluid mechanics. From the physical point of view, the investigation includes binary mixtures and two-point formulations suitable for describing turbulent flows. From the mathematical point of view, we reveal the Lie algebra structure involved in the p...

We show how to carry out the gauging of the Poisson sigma model in an AKSZ inspired formulation by coupling it to the a generalization of the Weil model worked out in ref. arXiv:0706.1289 [hep-th]. We call the resulting gauged field theory, Poisson--Weil sigma model. We study the BV cohomology of the model and show its relation to Hamiltonian basic and equivariant Poisson cohomology. As an application, we carry out the gauge fixing of the pure Weil model and of the Poisson--Weil model. In the first case, we obtain the 2--dimensional version of Donaldson--Witten topological gauge theory, describing the moduli space of flat connections on a closed surface. In the second case, we recover the gauged A topological sigma model worked out by Baptista describing the moduli space of solutions of the so--called vortex equations.

An immersed interface-enabled vortex particle-mesh (VPM) solver is presented for the simulation of 2-D incompressible viscous flows, in the framework of external aerodynamics. Considering the simulation of free vortical flows, such as wakes and jets, vortex particle-mesh methods already provide a valuable alternative to standard CFD methods, thanks to the interesting numerical properties arising from its Lagrangian nature. Yet, accounting for solid bodies remains challenging, despite the extensive research efforts that have been made for several decades. The present immersed interface approach aims at improving the consistency and the accuracy of one very common technique (based on Lighthill's model) for the enforcement of the no-slip condition at the wall in vortex methods. Targeting a sharp treatment of the wall calls for substantial modifications at all computational levels of the VPM solver. More specifically, the solution of the underlying Poisson equation, the computation of the diffusion term and the particle-mesh interpolation are adapted accordingly and the spatial accuracy is assessed. The immersed interface VPM solver is subsequently validated on the simulation of some challenging impulsively started flows, such as the flow past a cylinder and that past an airfoil. Research Fellow (PhD student) of the F.R.S.-FNRS of Belgium.

Full Text Available Sample coordination seeks to maximize or to minimize the overlap of two or more samples. The former is known as positive coordination, and the latter as negative coordination. Positive coordination is mainly used for estimation purposes and to reduce data collection costs. Negative coordination is mainly performed to diminish the response burden of the sampled units. Poisson sampling design with permanent random numbers provides an optimum coordination degree of two or more samples. The size of a Poisson sample is, however, random. Conditional Poisson (CP sampling is a modification of the classical Poisson sampling that produces a fixed-size πps sample. We introduce two methods to coordinate Conditional Poisson samples over time or simultaneously. The first one uses permanent random numbers and the list-sequential implementation of CP sampling. The second method uses a CP sample in the first selection and provides an approximate one in the second selection because the prescribed inclusion probabilities are not respected exactly. The methods are evaluated using the size of the expected sample overlap, and are compared with their competitors using Monte Carlo simulation. The new methods provide a good coordination degree of two samples, close to the performance of Poisson sampling with permanent random numbers.

The authors propose a parallel algebraic multilevel algorithm (AMG), which has the novel feature that the subproblem residing in each processor is defined over the entire partition domain, although the vast majority of unknowns for each subproblem are associated with the partition owned by the corresponding processor. This feature ensures that a global coarse description of the problem is contained within each of the subproblems. The advantages of this approach are that interprocessor communication is minimized in the solution process while an optimal order of convergence rate is preserved; and the speed of local subproblem solvers can be maximized using the best existing sequential algebraic solvers.

A new multigrid algorithm based on the method of self-correction for the solution of elliptic problems is described. The method exploits information contained in the residual to dynamically modify the source term (right-hand side) of the elliptic problem. It is shown that the self-correcting solver is more efficient at damping the short wavelength modes of the algebraic error than its standard equivalent. When used in conjunction with a multigrid method, the resulting solver displays an improved convergence rate with no additional computational work.

In this paper, we present a SAT solver based on the combination of DPLL (Davis Putnam Logemann and Loveland) algorithm and Failed Literal Detection (FLD), one of the advanced reasoning techniques. We propose a Dynamic Filtering method that consists of two restriction rules for FLD: internal and external filtering. The method reduces the number of tested literals in FLD and its computational time while maintaining the ability to find most of the failed literals in each decision level. Unlike the pre-defined criteria, literals are removed dynamically in our approach. In this way, our FLD can adapt itself to different real-life benchmarks. Many useless tests are therefore avoided and as a consequence it makes FLD fast. Some other static restrictions are also added to further improve the efficiency of FLD. Experiments show that our optimized FLD is much more efficient than other advanced reasoning techniques.

In this paper,we present a new edit tool for the user to conveniently preserve or freely edit the object appearance during seamless image composition.We observe that though Poisson image editing is effective for seamless image composition.Its color bleeding (the color of the target image is propagated into the source image) is not always desired in applications,and it provides no way to allow the user to edit the appearance of the source image.To make it more flexible and practical,we introduce new energy terms to control the appearance change,and integrate them into the Poisson image editing framework.The new energy function could still be realized using efficient sparse linear solvers,and the user can interactively refine the constraints.With the new tool,the user can enjoy not only seamless image composition,but also the flexibility to preserve or manipulate the appearance of the source image at the same time.This provides more potential for creating new images.Experimental results demonstrate the effectiveness of our new edit tool,with similar time cost to the original Poisson image editing.

A butterfly-based fast direct integral equation solver for analyzing high-frequency scattering from two-dimensional objects is presented. The solver leverages a randomized butterfly scheme to compress blocks corresponding to near- and far-field interactions in the discretized forward and inverse electric field integral operators. The observed memory requirements and computational cost of the proposed solver scale as O(Nlog^2N) and O(N^1.5 logN), respectively. The solver is applied to the analysis of scattering from electrically large objects spanning over ten thousand of wavelengths and modeled in terms of five million unknowns.

We consider time-changed Poisson processes, and derive the governing difference-differential equations (DDE) these processes. In particular, we consider the time-changed Poisson processes where the the time-change is inverse Gaussian, or its hitting time process, and discuss the governing DDE's. The stable subordinator, inverse stable subordinator and their iterated versions are also considered as time-changes. DDE's corresponding to probability mass functions of these time-changed processes are obtained. Finally, we obtain a new governing partial differential equation for the tempered stable subordinator of index $0Poisson process time-changed by tempered stable subordinator. Our results extend and complement the results in Baeumer et al. \\cite{B-M-N} and Beghin et al. \\cite{BO-1} in several directions.

Currently, Eulerian flow solvers are very efficient in accurately resolving flow structures near solid boundaries. On the other hand, they tend to be diffusive and to dampen high-intensity vortical structures after a short distance away from solid boundaries. The use of high order methods and fine grids, although alleviating this problem, gives rise to large systems of equations that are expensive to solve. Lagrangian solvers, as the regularized vortex particle method, have shown to eliminate (in practice) the diffusion in the wake. As a drawback, the modelling of solid boundaries is less accurate, more complex and costly than with Eulerian solvers (due to the isotropy of its computational elements). Given the drawbacks and advantages of both Eulerian and Lagrangian solvers the combination of both methods, giving rise to a hybrid solver, is advantageous. The main idea behind the hybrid solver presented is the following. In a region close to solid boundaries the flow is solved with an Eulerian solver, where th...

Main characteristics of stationary anisotropic Poisson processes of cylinders (dilated k-dimensional flats) in d-dimensional Euclidean space are studied. Explicit formulae for the capacity functional, the covariance function, the contact distribution function, the volume fraction, and the intensity of the surface area measure are given which can be used directly in applications.

We show that the calculation of Berezin integrals over anticommuting variables can be reduced to the evaluation of expectations of functionals of Poisson processes via an appropriate Feynman-Kac formula. In this way the tools of ordinary analysis can be applied to Berezin integrals and, as an example, we prove a simple upper bound. Possible applications of our results are briefly mentioned.

Deblurring noisy Poisson images has recently been a subject of an increasing amount of works in many areas such as astronomy and biological imaging. In this paper, we focus on confocal microscopy, which is a very popular technique for 3-D imaging of biological living specimens that gives images with a very good resolution (several hundreds of nanometers), although degraded by both blur and Poisson noise. Deconvolution methods have been proposed to reduce these degradations, and in this paper, we focus on techniques that promote the introduction of an explicit prior on the solution. One difficulty of these techniques is to set the value of the parameter, which weights the tradeoff between the data term and the regularizing term. Only few works have been devoted to the research of an automatic selection of this regularizing parameter when considering Poisson noise; therefore, it is often set manually such that it gives the best visual results. We present here two recent methods to estimate this regularizing parameter, and we first propose an improvement of these estimators, which takes advantage of confocal images. Following these estimators, we secondly propose to express the problem of the deconvolution of Poisson noisy images as the minimization of a new constrained problem. The proposed constrained formulation is well suited to this application domain since it is directly expressed using the antilog likelihood of the Poisson distribution and therefore does not require any approximation. We show how to solve the unconstrained and constrained problems using the recent alternating-direction technique, and we present results on synthetic and real data using well-known priors, such as total variation and wavelet transforms. Among these wavelet transforms, we specially focus on the dual-tree complex wavelet transform and on the dictionary composed of curvelets and an undecimated wavelet transform.

We present a numerical scheme that can be combined with any fixed boundary finite element based Poisson or Grad–Shafranov solver to compute the first and second partial derivatives of the solution to these equations with the same order of convergence as the solution itself. At the heart of our scheme is an efficient and accurate computation of the Dirichlet to Neumann map through the evaluation of a singular volume integral and the solution to a Fredholm integral equation of the second kind. Our numerical method is particularly useful for magnetic confinement fusion simulations, since it allows the evaluation of quantities such as the magnetic field, the parallel current density and the magnetic curvature with much higher accuracy than has been previously feasible on the affordable coarse grids that are usually implemented.

Modern geoelectrical data acquisition systems allow large amounts of data to be collected in a short time. Inversions of such data sets require powerful forward solvers for predicting the electrical potentials. State-of-the-art solvers are typically based on finite elements. Recent developments in numerical mathematics led to direct matrix solvers that allow the equation systems arising from such finite element problems to be solved very efficiently. They are particularly useful for 3-D geoelectrical problems, where many electrodes are involved. Although modern direct matrix solvers include optimized memory saving strategies, their application to realistic, large-scale 3-D problems is still somewhat limited. Therefore, we present two novel techniques that allow the number of gridpoints to be reduced considerably, while maintaining a high solution accuracy. In the areas surrounding an electrode array we attach infinite elements that continue the electrical potentials to infinity. This does not only reduce the number of gridpoints, but also avoids the artificial Dirichlet or mixed boundary conditions that are well known to be the cause of numerical inaccuracies. Our second development concerns the singularity removal in the presence of significant surface topography. We employ a fast multipole boundary element method for computing the singular potentials. This renders unnecessary mesh refinements near the electrodes, which results in substantial savings of gridpoints of up to more than 50 per cent. By means of extensive numerical tests we demonstrate that combined application of infinite elements and singularity removal allows the number of gridpoints to be reduced by a factor of ~6-10 compared with traditional finite element methods. This will be key for applying finite elements and direct matrix solver techniques to realistic 3-D inversion problems.

In this thesis, we reexamine the long discussion on which model is suitable for studying Internet traffic: Poisson or Long-tailed Internet traffic. Poisson model, adapted from telephone network, has been used since the beginning of World Wide Web, while long-tailed distribution gradually takes over with believable evidence. Instead of using Superposition of Point Processes to explain why traffic that is not Poisson tends towards Poisson traffic as the load increases, as it is recent...

Adaptive Mesh Refinement (AMR) is a numerical technique for locally tailoring the resolution computational grids. Multilevel algorithms for solving elliptic problems on adaptive grids include the Fast Adaptive Composite grid method (FAC) and its parallel variants (AFAC and AFACx). Theory that confirms the independence of the convergence rates of FAC and AFAC on the number of refinement levels exists under certain ellipticity and approximation property conditions. Similar theory needs to be developed for AFACx. The effectiveness of multigrid-based elliptic solvers such as FAC, AFAC, and AFACx on adaptively refined overlapping grids is not clearly understood. Finally, a non-trivial eye model problem will be solved by combining the power of using overlapping grids for complex moving geometries, AMR, and multilevel elliptic solvers.

Providing security guarantees for wireless communication is critically important for today's applications. While previous work in this area has concentrated on radio frequency (RF) channels, providing security guarantees for RF channels is inherently difficult because they are prone to rapid variations due small scale fading. Wireless optical communication, on the other hand, is inherently more secure than RF communication due to the intrinsic aspects of the signal propagation in the optical and near-optical frequency range. In this paper, secure communication over wireless optical links is examined by studying the secrecy capacity of a direct detection system. For the degraded Poisson wiretap channel, a closed-form expression of the secrecy capacity is given. A complete characterization of the general rate-equivocation region is also presented. For achievability, an optimal code is explicitly constructed by using the structured code designed by Wyner for the Poisson channel. The converse is proved in two dif...

We consider a Poisson process $\\Phi$ on a general phase space. The expectation of a function of $\\Phi$ can be considered as a functional of the intensity measure $\\lambda$ of $\\Phi$. Extending ealier results of Molchanov and Zuyev (2000) on finite Poisson processes, we study the behaviour of this functional under signed (possibly infinite) perturbations of $\\lambda$. In particular we obtain general Margulis--Russo type formulas for the derivative with respect to non-linear transformations of the intensity measure depending on some parameter. As an application we study the behaviour of expectations of functions of multivariate pure jump L\\'evy processes under perturbations of the L\\'evy measure. A key ingredient of our approach is the explicit Fock space representation obtained in Last and Penrose (2011).

In Computer Science, the Boolean Satisfiability Problem(SAT) is the problem of determining if there exists an interpretation that satisfies a given Boolean formula. SAT is one of the first problems that was proven to be NP-complete, which is also fundamental to artificial intelligence, algorithm and hardware design. This paper reviews the main algorithms of the SAT solver in recent years, including serial SAT algorithms, parallel SAT algorithms, SAT algorithms based on GPU, and SAT algorithms based on FPGA. The development of SAT is analyzed comprehensively in this paper. Finally, several possible directions for the development of the SAT problem are proposed.

We investigate the performance of a hybrid plasma solver on the test problem of an ion beam. The parallel solver is based on cell centered finite differences in space, and a predictor-corrector leapfrog scheme in time. The implementation is done in the FLASH software framework. It is shown that the solver conserves energy well over time, and that the parallelization is efficient (it exhibits weak scaling).

We present an extension of the HLLC approximate Riemann solver by Toro, Spruce and Speares to the relativistic equations of fluid dynamics. The solver retains the simplicity of the original two-wave formulation proposed by Harten, Lax and van Leer (HLL) but it restores the missing contact wave in the solution of the Riemann problem. The resulting numerical scheme is computationally efficient, robust and positively conservative. The performance of the new solver is evaluated through numerical testing in one and two dimensions.

Highlights: • The two-fluid model and the challenges associated with its numerical modeling are investigated. • A high-order solver based on flux limiter schemes and the theta method was developed. • The solver was compared to existing thermal hydraulics codes used in nuclear industry. • The solver was shown to handle fast transients with discontinuities and phase change. - Abstract: Finite volume techniques with staggered mesh are used to develop a new numerical solver for the one-dimensional two-phase two-fluid model using a high-resolution, Total Variation Diminishing (TVD) scheme. The solver is implemented to analyze numerical benchmark problems for verification and testing its abilities to handle discontinuities and fast transients with phase change. Convergence rates are investigated by comparing numerical results to analytical solutions available in literature for the case of the faucet flow problem. The solver based on a new TVD scheme is shown to exhibit higher-order of accuracy compared to other numerical schemes. Mass errors are also examined when phase change occurs for the shock tube problem, and compared to those of the 1st-order upwind scheme implemented in the nuclear thermal-hydraulics code TRACE. The solver is shown to exhibit numerical stability when applied to problems with discontinuous solutions and results of the new solver are free of spurious oscillations.

Full Text Available The Why3 IDE and verification system facilitates the use of a wide range of Satisfiability Modulo Theories (SMT solvers through a driver-based architecture. We present Where4: a portfolio-based approach to discharge Why3 proof obligations. We use data analysis and machine learning techniques on static metrics derived from program source code. Our approach benefits software engineers by providing a single utility to delegate proof obligations to the solvers most likely to return a useful result. It does this in a time-efficient way using existing Why3 and solver installations - without requiring low-level knowledge about SMT solver operation from the user.

We are developing multigrid methods that will efficiently solve elliptic problems with anisotropic and discontinuous coefficients on adaptive grids. The final product will be a library that provides for the simplified solution of such problems. This library will directly benefit the efforts of other Laboratory groups. The focus of this work is research on serial and parallel elliptic algorithms and the inclusion of our black-box multigrid techniques into this new setting. The approach applies the Los Alamos object-oriented class libraries that greatly simplify the development of serial and parallel adaptive mesh refinement applications. In the final year of this LDRD, we focused on putting the software together; in particular we completed the final AMR++ library, we wrote tutorials and manuals, and we built example applications. We implemented the Fast Adaptive Composite Grid method as the principal elliptic solver. We presented results at the Overset Grid Conference and other more AMR specific conferences. We worked on optimization of serial and parallel performance and published several papers on the details of this work. Performance remains an important issue and is the subject of continuing research work.

In this paper we present a fast explicit solver for solution of non-stationary problems using L2 projections with isogeometric finite element method. The solver has been implemented within GALOIS framework. It enables parallel multi-core simulations of different time-dependent problems, in 1D, 2D, or 3D. We have prepared the solver framework in a way that enables direct implementation of the selected PDE and corresponding boundary conditions. In this paper we describe the installation, implementation of exemplary three PDEs, and execution of the simulations on multi-core Linux cluster nodes. We consider three case studies, including heat transfer, linear elasticity, as well as non-linear flow in heterogeneous media. The presented package generates output suitable for interfacing with Gnuplot and ParaView visualization software. The exemplary simulations show near perfect scalability on Gilbert shared-memory node with four Intel® Xeon® CPU E7-4860 processors, each possessing 10 physical cores (for a total of 40 cores).

Full Text Available After a brief summary of the main properties of Poisson manifolds and Lie algebroids in general, we survey recent work on the modular classes of Poisson and twisted Poisson manifolds, of Lie algebroids with a Poisson or twisted Poisson structure, and of Poisson-Nijenhuis manifolds. A review of the spinor approach to the modular class concludes the paper.

This paper presents an efficient parallel multigrid solver for speeding up the computation of a 3-D model that treats the flow of a viscous fluid over a flat plate. The main interest of this simulation lies in exhibiting some basic difficulties that prevent optimal multigrid efficiencies from being achieved. As the computing platform, we have used Coral, a Beowulf-class system based on Intel Pentium processors and equipped with GigaNet cLAN and switched Fast Ethernet networks. Our study not only examines the scalability of the solver but also includes a performance evaluation of Coral where the investigated solver has been used to compare several of its design choices, namely, the interconnection network (GigaNet versus switched Fast-Ethernet) and the node configuration (dual nodes versus single nodes). As a reference, the performance results have been compared with those obtained with the NAS-MG benchmark.

A parallel fast direct solver for rank-compressible block tridiagonal linear systems is presented. Algorithmic synergies between Cyclic Reduction and Hierarchical matrix arithmetic operations result in a solver with O(Nlog2N) arithmetic complexity and O(NlogN) memory footprint. We provide a baseline for performance and applicability by comparing with well-known implementations of the $$\\\\mathcal{H}$$ -LU factorization and algebraic multigrid within a shared-memory parallel environment that leverages the concurrency features of the method. Numerical experiments reveal that this method is comparable with other fast direct solvers based on Hierarchical Matrices such as $$\\\\mathcal{H}$$ -LU and that it can tackle problems where algebraic multigrid fails to converge.

Finite element analyses of electromagnetic field are commonly used for designing of various electronic devices. The scale of the analyses becomes larger and larger, therefore, a fast linear solver is needed to solve linear equations arising from the finite element method. Since a multigrid solver is the fastest linear solver for these problems, parallelization of a multigrid solver is a quite useful approach. From the viewpoint of industrial applications, an effective usage of a small-scale PC cluster is important due to initial cost for introducing parallel computers. In this paper, a distributed parallel multigrid solver for a small-scale PC cluster is developed. In high frequency electromagnetic field analyses, a special block Gauss-Seidel smoother is used for the multigrid solver instead of general smoothers such as Gauss-Seidel smoother or Jacobi smoother in order to improve a convergence rate. The block multicolor ordering technique is applied to parallelize the smoother. A numerical exsample shows that a 3.7-fold speed-up in computational time and a 3.0-fold increase in the scale of the analysis were attained when the number of CPU was increased from one to five.

We present a five-wave Riemann solver for the equations of ideal relativistic magneto-hydrodynamics. Our solver can be regarded as a relativistic extension of the five-wave HLLD Riemann solver initially developed by Miyoshi & Kusano for the equations of ideal magnetohydrodynamics. The solution to the Riemann problem is approximated by a five-wave pattern, comprising two outermost fast shocks, two rotational discontinuities and a contact surface in the middle. The proposed scheme is considerably more elaborate than in the classical case since the normal velocity is no longer constant across the rotational modes. Still, proper closure to the Rankine-Hugoniot jump conditions can be attained by solving a non-linear scalar equation in the total pressure variable which, for the chosen configuration, has to be constant over the whole Riemann fan. The accuracy of the new Riemann solver is validated against one-dimensional tests and multidimensional applications. It is shown that our new solver considerably improves over the popular Harten-Lax-van Leer solver or the recently proposed HLLC schemes.

We present large deviation results for two versions of fractional Poisson processes: the main version which is a renewal process, and the alternative version where all the random variables are weighted Poisson distributed. We also present a sample path large deviation result for suitably normalized counting processes; finally we show how this result can be applied to the two versions of fractional Poisson processes considered in this paper.

For spacecrafts the concept of ion thrusters presents a very efficient method of propulsion. Optimization of thrusters is imperative, but experimental access is difficult. Plasma simulations offer means to understand the plasma physics within an ion thruster and can aid the design of new thruster concepts. In order to achieve best simulation performances, code optimizations and parallelization strategies need to be investigated. In this work the role of different solution strategies for Poisson's equation in electrostatic Particle-in-Cell simulations of the HEMP-DM3a ion thruster was studied. The direct solution method of LU decomposition is compared to a stationary iterative method, the successive over-relaxation solver. Results and runtime of solvers were compared, and an outlook on further improvements and developments is presented. This work was supported by the German Space Agency DLR through Project 50RS1510..

A new, momentum preserving fastPoissonsolver for N-body systems sharing effective O(N) computational complexity, has been recently developed by Dehnen (2000, 2002). We have implemented the proposed algorithms in a Fortran-90 code, and parallelized it by a domain decomposition using the MPI routines. The code has been applied to intensive numerical investigations of galaxy mergers, in particular focusing on the possible origin of some of the observed scaling relations of elliptical galaxies. We found that the Fundamental Plane is preserved by an equal mass merging hierarchy, while it is not in a scenario where galaxies grow by accretion of smaller stellar systems. In addition, both the Faber-Jackson and Kormendy relations are not reproduced by our simulations.

We present and analyze a modified Newton solver, the so called operator-related damped Jacobian method, with a line search globalization for the solution of the strongly nonlinear momentum equation in a viscous-plastic (VP) sea ice model.Due to large variations in the viscosities, the resulting nonlinear problem is very difficult to solve. The development of fast, robust and converging solvers is subject to present research. There are mainly three approaches for solving the nonlinear momentum equation of the VP model, a fixed-point method denoted as Picard solver, an inexact Newton method and a subcycling procedure based on an elastic-viscous-plastic model approximation. All methods tend to have problems on fine meshes by sharp structures in the solution. Convergence rates deteriorate such that either too many iterations are required to reach sufficient accuracy or convergence is not obtained at all.To improve robustness globalization and acceleration approaches, which increase the area of fast convergence, are needed. We develop an implicit scheme with improved convergence properties by combining an inexact Newton method with a Picard solver. We derive the full Jacobian of the viscous-plastic sea ice momentum equation and show that the Jacobian is a positive definite matrix, guaranteeing global convergence of a properly damped Newton iteration. We compare our modified Newton solver with line search damping to an inexact Newton method with established globalization and acceleration techniques. We present a test case that shows improved robustness of our new approach, in particular on fine meshes.

Sudoku, also known as Number Place, is a logic-based placement puzzle. The aim of the puzzle is to enter a numerical digit from 1 through 9 in each cell of a 9 x 9 grid made up of 3 x 3 subgrids (called ''regions''), starting with various digits given in some cells (the ''givens''). Each row, column, and region must contain only one instance of each numeral. Completing the puzzle requires patience and logical ability. Although first published in a U.S. puzzle magazine in 1979, Sudoku initially caught on in Japan in 1986 and attained international popularity in 2005. Last fall, after noticing Sudoku puzzles in some newspapers and magazines, I attempted a few just to see how hard they were. Of course, the difficulties varied considerably. ''Obviously'' one could use Trial and Error but all the advice was to ''Use Logic''. Thinking to flex, and strengthen, those powers, I began to tackle the puzzles systematically. That is, when I discovered a new tactical rule, I would write it down, eventually generating a list of ten or so, with some having overlap. They served pretty well except for the more difficult puzzles, but even then I managed to develop an additional three rules that covered all of them until I hit the Oregonian puzzle shown. With all of my rules, I could not seem to solve that puzzle. Initially putting my failure down to rapid mental fatigue (being unable to hold a sufficient quantity of information in my mind at one time), I decided to write a program to implement my rules and see what I had failed to notice earlier. The solver, too, failed. That is, my rules were insufficient to solve that particular puzzle. I happened across a book written by a fellow who constructs such puzzles and who claimed that, sometimes, the only tactic left was trial and error. With a trial and error routine implemented, my solver successfully completed the Oregonian puzzle, and has successfully

Several SIERRA applications make use of third-party libraries to solve systems of linear and nonlinear equations, and to solve eigenproblems. The classes and interfaces in the SIERRA framework that provide linear system assembly services and access to solver libraries are collectively referred to as solver services. This paper provides an overview of SIERRA's solver services including the design goals that drove the development, and relationships and interactions among the various classes. The process of assembling and manipulating linear systems will be described, as well as access to solution methods and other operations.

We present a computationally efficient, adaptive solver for the solution of the Poisson and Helmholtz equation used in flow simulations in domains with combinations of unbounded and periodic directions. The method relies on using FFTs on an extended domain and it is based on the method proposed by Hockney and Eastwood for plasma simulations. The method is well-suited to problems with dynamically growing domains and in particular flow simulations using vortex particle methods. The efficiency of the method is demonstrated in simulations of trailing vortices.

The purpose of this article is to benchmark different optimization solvers when applied to various finite element based structural topology optimization problems. An extensive and representative library of minimum compliance, minimum volume, and mechanism design problem instances for different...... sizes is developed for this benchmarking. The problems are based on a material interpolation scheme combined with a density filter. Different optimization solvers including Optimality Criteria (OC), the Method of Moving Asymptotes (MMA) and its globally convergent version GCMMA, the interior point...... profiles conclude that general solvers are as efficient and reliable as classical structural topology optimization solvers. Moreover, the use of the exact Hessians in SAND formulations, generally produce designs with better objective function values. However, with the benchmarked implementations solving...

We describe the first implementation of the all-electron Kohn-Sham density functional periodic solver (DFT) using multi-wavelets and fast integral equations using MADNESS (multiresolution adaptive numerical environment for scientific simulation; http://code.google.com/p/m-a-d-n-e-s-s). The multiresolution nature of a multi-wavelet basis allows for fast computation with guaranteed precision. By reformulating the Kohn-Sham eigenvalue equation into the Lippmann-Schwinger equation, we can avoid using the derivative operator which allows better control of overall precision for the all-electron problem. Other highlights include the development of periodic integral operators with low-rank separation, an adaptable model potential for nuclear potential, and an implementation for Hartree Fock exchange. This work was supported by NSF project OCI-0904972 and made use of resources at the Center for Computational Sciences at Oak Ridge National Laboratory under contract DE-AC05-00OR22725.

The theory of rigid body motion with emphasis on the modifications introduced by a Cardan suspension is outlined. The configuration space is no longer SO(3) but a 3-torus; the equivalent of the Poisson sphere, after separation of an angular variable, is a Poisson torus. Iso-energy surfaces and their bifurcations are discussed. A universal Poincaré section method is proposed.

We present proofs of classical results in Poisson geometry using techniques from Dirac geometry. This article is based on mini-courses at the Poisson summer school in Geneva, June 2016, and at the workshop "Quantum Groups and Gravity" at the University of Waterloo, April 2016.

In order to simulate large-scale ground water flow problems more efficiently with MODFLOW, the OpenMP programming paradigm was used to parallelize the preconditioned conjugate-gradient (PCG) solver with in this study. Incremental parallelization, the significant advantage supported by OpenMP on a shared-memory computer, made the solver transit to a parallel program smoothly one block of code at a time. The parallel PCG solver, suitable for both MODFLOW-2000 and MODFLOW-2005, is verified using an 8-processor computer. Both the impact of compilers and different model domain sizes were considered in the numerical experiments. Based on the timing results, execution times using the parallel PCG solver are typically about 1.40 to 5.31 times faster than those using the serial one. In addition, the simulation results are the exact same as the original PCG solver, because the majority of serial codes were not changed. It is worth noting that this parallelizing approach reduces cost in terms of software maintenance because only a single source PCG solver code needs to be maintained in the MODFLOW source tree.

In general, a SAT Solver based on conflict-driven DPLL consists of variable selection, phase selection, Boolean Constraint Propagation, conflict analysis, clause learning and its database maintenance. Optimizing any part of these components can enhance the performance of a solver. This paper focuses on optimizing phase selection. Although the ACE (Approximation of the Combined lookahead Evaluation) weight is applied to a lookahead SAT solver such as March, so far, no conflict-driven SAT solver applies successfully the ACE weight, since computing the ACE weight is time-consuming. Here we apply the ACE weight to partial phase selection of conflict-driven SAT solvers. This can be seen as an improvement of the heuristic proposed by Jeroslow-Wang (1990). We incorporate the ACE heuristic and the existing phase selection heuristics in the new solver MPhaseSAT, and select a phase heuristic in a way similar to portfolio methods. Experimental results show that adding the ACE heuristic can improve the conflict-driven so...

Increasingly large chemical mechanisms are needed to predict autoignition, heat release and pollutant emissions in computational fluid dynamics (CFD) simulations of in-cylinder processes in compression-ignition engines and other applications. Calculation of chemical source terms usually dominates the computational effort, and several strategies have been proposed to reduce the high computational cost associated with realistic chemistry in CFD. Central to most strategies is a stiff ordinary differential equation (ODE) solver to compute the change in composition due to chemical reactions over a computational time step. Most work to date on stiff ODE solvers for computational combustion has focused on backward differential formula (BDF) methods, and has not explicitly considered the implications of how the stiff ODE solver couples with the CFD algorithm. In this work, a fresh look at stiff ODE solvers is taken that includes how the solver is integrated into a turbulent combustion CFD code, and the advantages of extrapolation-based solvers in this regard are demonstrated. Benefits in CPU time and accuracy are demonstrated for homogeneous systems and compression-ignition engines, for chemical mechanisms that range in size from fewer than 50 to more than 7,000 species.

This paper describes an efficient model of an antenna system for microwave imaging. The authors present techniques employed in the process of preparation of this model, as well as an accuracy comparison with the working prototype system....

This paper describes an efficient model of an antenna system for microwave imaging. The authors present techniques employed in the process of preparation of this model, as well as an accuracy comparison with the working prototype system....

This paper presents evidence that six of the seven parts of speech occur in written text as Poisson processes, simple or recurring. The six major parts are nouns, verbs, adjectives, adverbs, prepositions, and conjunctions, with the interjection occurring too infrequently to support a model. The data consist of more than the first 5000 words of works by four major authors coded to label the parts of speech, as well as periods (sentence terminators). Sentence length is measured via the period and found to be normally distributed with no stochastic model identified for its occurrence. The models for all six speech parts but the noun significantly distinguish some pairs of authors and likewise for the joint use of all words types. Any one author is significantly distinguished from any other by at least one word type and sentence length very significantly distinguishes each from all others. The variety of word type use, measured by Shannon entropy, builds to about 90% of its maximum possible value. The rate constants for nouns are close to the fractions of maximum entropy achieved. This finding together with the stochastic models and the relations among them suggest that the noun may be a primitive organizer of written text.

In Model Predictive Control (MPC), an optimization problem needs to be solved at each sampling time, and this has traditionally limited use of MPC to systems with slow dynamic. In recent years, there has been an increasing interest in the area of fast small-scale solvers for linear MPC......, with the two main research areas of explicit MPC and tailored on-line MPC. State-of-the-art solvers in this second class can outperform optimized linear-algebra libraries (BLAS) only for very small problems, and do not explicitly exploit the hardware capabilities, relying on compilers for that. This approach...... problems 2 to 8 times faster than the current state-of-the-art solver for this class of problems, and the high-performance is maintained for MPC problems with up to a few hundred states....

legacy codes are not always easily parallelized and the time spent on conversion might not pay o in the end. We present a highly generic C++ library for fast assembling of partial differential equation (PDE) solvers, aiming at utilizing the computational resources of GPUs. The library requires a minimum......, two important features for ecient GPU utilization and for enabling solution of large problems. In order to solve the large linear systems of equations, arising from the discretization of PDEs, the library includes a set of common iterative solvers. All iterative solvers are based on template arguments...... of fully nonlinear free surface water waves over uneven depths[1, 2, 3]. The wave model is based on the potential ow formulation, with the computational bottleneck of solving a fully three dimensional Laplace problem eciently. A robust h- or p-multigrid preconditioned defect correction method is applied...

Jacobi - Davidson, and FEAST), establishing the competitiveness of my methods . Graduate School Form 30 Updated 1/15/2015 PURDUE UNIVERSITY GRADUATE...LOBPCG, Jacobi -Davidson, and FEAST), establishing the competitiveness of our methods . 1 1 INTRODUCTION Many applications in science and engineering give...though SLEPc’s Jacobi -Davidson is the fastest method ; it is roughly twice as fast as TraceMin-Davidson. However, since it uses a block size 90 of 1

The fractional Poisson process (FPP) is a counting process with independent and identically distributed inter-event times following the Mittag-Leffler distribution. This process is very useful in several fields of applied and theoretical physics including models for anomalous diffusion. Contrary to the well-known Poisson process, the fractional Poisson process does not have stationary and independent increments. It is not a L\\'evy process and it is not a Markov process. In this letter, we present formulae for its finite-dimensional distribution functions, fully characterizing the process. These exact analytical results are compared to Monte Carlo simulations.

Collisionless space plasmas often deviate from Maxwellian-like velocity distributions. To study kinetic waves and instabilities in such plasmas, the dispersion relation, which depends on the velocity distribution, needs to be solved numerically. Most current dispersion solvers (e.g. WHAMP) take advantage of mathematical properties of the Gaussian (or generalized Lorentzian) function, and assume that the velocity distributions can be modeled by a combination of several drift-Maxwellian (or drift-Lorentzian) components. In this study we are developing a kinetic dispersion solver that admits nearly arbitrary non-relativistic parallel velocity distributions. A key part of any dispersion solver is the evaluation of a Hilbert transform of the velocity distribution function and its derivative along Landau contours. Our new solver builds upon a recent method to compute the Hilbert transform accurately and efficiently using the fast Fourier transform, while simultaneously treating the singularities arising from resonances analytically. We have benchmarked our new solver against other codes dealing with Maxwellian distributions. As an example usage of our code, we will show results for several instabilities that occur for electron velocity distributions observed in the solar wind.

The recent research progress in the area of plant design and simulation highlighted the importance of integrating design and analysis models on a unified environment. For currently developed advanced reactors, either for power production or research, this effort has embraced impressive state-of-the-art information and automation technology. The PEACER (Proliferation-resistant, Environment friendly, Accident-tolerant, Continual and Economical Reactor) is one of the conceptual fast reactor system cooled by LBE (Lead Bismuth Eutectic) for nuclear waste transmutation. This reactor system is composed of innovative combination between design process and analysis. To establish an integrated design process by coupling design, analysis, and post-processing technology while minimizing the repetitive and costly manual interactions for design changes, a solver interfaced virtual reality simulation system (SIVR) has been developed for a nuclear transmutation energy system as PEACER. The SIVR was developed using Virtual Reality Modeling Language (VRML) in order to interface a commercial 3D CAD tool with various engineering solvers and to implement virtual reality presentation of results in a neutral format. In this paper, we have shown the SIVR approach viable and effective in the life-cycle management of complex nuclear energy systems, including design, construction and operation. For instance, The HELIOS is a down scaled model of the PEACER prototype to demonstrate the operability and safety as well as preliminary test of PEACER PLM (Product Life-cycle Management) with SIVR (Solver Interfaced Virtual Reality) concepts. Most components are designed by CATIA, which is 3D CAD tool. During the construction, 3D drawing by CATIA was effective to handle and arrange the loop configuration, especially when we changed the design. Most of all, This system shows the transparency of design and operational status of an energy complex to operators and inspectors can help ensure accident

Full Text Available We present a new scheme for solving the ionospheric boundary conditions required in magnetospheric MHD simulations. In contrast to the electrostatic ionospheric solvers currently in use, the new solver takes ionospheric induction into account by solving Faraday's law simultaneously with Ohm's law and current continuity. From the viewpoint of an MHD simulation, the new inductive solver is similar to the electrostatic solvers, as the same input data is used (field-aligned current [FAC] and ionospheric conductances and similar output is produced (ionospheric electric field. The inductive solver is tested using realistic, databased models of an omega-band and westward traveling surge. Although the tests were performed with local models and MHD simulations require a global ionospheric solution, we may nevertheless conclude that the new solution scheme is feasible also in practice. In the test cases the difference between static and electrodynamic solutions is up to ~10 V km−1 in certain locations, or up to 20-40% of the total electric field. This is in agreement with previous estimates. It should also be noted that if FAC is replaced by the ground magnetic field (or ionospheric equivalent current in the input data set, exactly the same formalism can be used to construct an inductive version of the KRM method originally developed by Kamide et al. (1981.

We present a new scheme for solving the ionospheric boundary conditions required in magnetospheric MHD simulations. In contrast to the electrostatic ionospheric solvers currently in use, the new solver takes ionospheric induction into account by solving Faraday's law simultaneously with Ohm's law and current continuity. From the viewpoint of an MHD simulation, the new inductive solver is similar to the electrostatic solvers, as the same input data is used (field-aligned current [FAC] and ionospheric conductances) and similar output is produced (ionospheric electric field). The inductive solver is tested using realistic, databased models of an omega-band and westward traveling surge. Although the tests were performed with local models and MHD simulations require a global ionospheric solution, we may nevertheless conclude that the new solution scheme is feasible also in practice. In the test cases the difference between static and electrodynamic solutions is up to ~10 V km-1 in certain locations, or up to 20-40% of the total electric field. This is in agreement with previous estimates. It should also be noted that if FAC is replaced by the ground magnetic field (or ionospheric equivalent current) in the input data set, exactly the same formalism can be used to construct an inductive version of the KRM method originally developed by Kamide et al. (1981).

Many researchers compute surface maps of the electrostatic potential (φ) with the Poisson-Boltzmann (PB) equation to relate the structural information obtained from X-ray and NMR experiments to biomolecular functions. Here we demonstrate that the usual method of obtaining these surface maps of φ, by interpolating from neighboring grid points on the solution grid generated by a PB solver, generates large errors because of the large discontinuity in the dielectric constant (and thus in the normal derivative of φ) at the surface. The Cartesian Poisson-Boltzmann solver contains several features that reduce the numerical noise in surface maps of φ: First, CPB introduces additional mesh points at the Cartesian grid/surface intersections where the PB equation is solved. This procedure ensures that the solution for interior mesh points only references nodes on the interior or on the surfaces; similarly for exterior points. Second, for added points on the surface, a second order least-squares reconstruction (LSR) is implemented that analytically incorporates the discontinuities at the surface. LSR is used both during the solution phase to compute φ at the surface and during postprocessing to obtain φ, induced charges, and ionic pressures. Third, it uses an adaptive grid where the finest grid cells are located near the molecular surface.

The portable software FoSSI is introduced that—in combination with additional free solver software packages—allows for an efficient and scalable parallel solution of large sparse linear equations systems arising in finite element model codes. FoSSI is intended to support rapid model code development, completely hiding the complexity of the underlying solver packages. In particular, the model developer need not be an expert in parallelization and is yet free to switch between different solver packages by simple modifications of the interface call. FoSSI offers an efficient and easy, yet flexible interface to several parallel solvers, most of them available on the web, such as PETSC, AZTEC, MUMPS, PILUT and HYPRE. FoSSI makes use of the concept of handles for vectors, matrices, preconditioners and solvers, that is frequently used in solver libraries. Hence, FoSSI allows for a flexible treatment of several linear equations systems and associated preconditioners at the same time, even in parallel on separate MPI-communicators. The second special feature in FoSSI is the task specifier, being a combination of keywords, each configuring a certain phase in the solver setup. This enables the user to control a solver over one unique subroutine. Furthermore, FoSSI has rather similar features for all solvers, making a fastsolver intercomparison or exchange an easy task. FoSSI is a community software, proven in an adaptive 2D-atmosphere model and a 3D-primitive equation ocean model, both formulated in finite elements. The present paper discusses perspectives of an OpenMP-implementation of parallel iterative solvers based on domain decomposition methods. This approach to OpenMP solvers is rather attractive, as the code for domain-local operations of factorization, preconditioning and matrix-vector product can be readily taken from a sequential implementation that is also suitable to be used in an MPI-variant. Code development in this direction is in an advanced state under

A common computational task is solving a set of ordinary differential equations (o.d.e.'s). A little known theorem says that the solution of any set of o.d.e.'s is exactly solved by the expectation value over a set of arbitary Poisson processes of a particular function of the elements of the matrix that defines the o.d.e.'s. The theorem thus provides a new starting point to develop real and imaginary-time continous-time solvers for quantum Monte Carlo algorithms, and several simple observations enable various quantum Monte Carlo techniques and variance reduction methods to transfer to a new context. I will state the theorem, note a transformation to a very simple computational scheme, and illustrate the use of some techniques from the directed-loop algorithm in context of the wavefunction Monte Carlo method that is used to solve the Lindblad master equation for the dynamics of open quantum systems. I will end by noting that as the theorem does not depend on the source of the o.d.e.'s coming from quantum mechanics, it also enables the transfer of continuous-time methods from quantum Monte Carlo to the simulation of various classical equations of motion heretofore only solved deterministically.

We introduce a new type of algebra which is called a Loday-Poisson algebra. The class of the Loday-Poisson algebras forms a special subclass of Aguiar's dual-prePoisson algebas (\\cite{A}). We will prove that there exists a unique Loday-Poisson algebra over a Loday algebra, like the Lie-Poisson algebra over a Lie algebra. Thus, Loday-Poisson algebras are regarded as noncommutative analogues of Lie-Poisson algebras. We will show that the polinomial Loday-Poisson algebra is deformation quantizable and that the associated quantum algebra is Loday's associative dialgebra.

Transitions to universality classes of random matrix ensembles have been useful in the study of weakly-broken symmetries in quantum chaotic systems. Transitions involving Poisson as the initial ensemble have been particularly interesting. The exact two-point correlation function was derived by one of the present authors for the Poisson to circular unitary ensemble (CUE) transition with uniform initial density. This is given in terms of a rescaled symmetry breaking parameter Λ. The same result was obtained for Poisson to Gaussian unitary ensemble (GUE) transition by Kunz and Shapiro, using the contour-integral method of Brezin and Hikami. We show that their method is applicable to Poisson to CUE transition with arbitrary initial density. Their method is also applicable to the more general ℓ CUE to CUE transition where CUE refers to the superposition of ℓ independent CUE spectra in arbitrary ratio.

Materials with negative Poisson's ratio attract considerable attention due to their underlying intriguing physical properties and numerous promising applications, particularly in stringent environments such as aerospace and defense areas, because of their unconventional mechanical enhancements. Recent progress in materials with a negative Poisson's ratio are reviewed here, with the current state of research regarding both theory and experiment. The inter-relationship between the underlying structure and a negative Poisson's ratio is discussed in functional materials, including macroscopic bulk, low-dimensional nanoscale particles, films, sheets, or tubes. The coexistence and correlations with other negative indexes (such as negative compressibility and negative thermal expansion) are also addressed. Finally, open questions and future research opportunities are proposed for functional materials with negative Poisson's ratios.

This overview of non-homogeneous and multidimensional Poisson point processes and their applications features mathematical tools and applications from emission- and transmission-computed tomography to multiple target tracking and distributed sensor detection.

A characterization of mixed Poisson processes in terms of disintegrations is proven. As a consequence some further characterizations of such processes via claim interarrival processes, martingales and claim measures are obtained.

A novel preconditioning scheme for electromagnetic scattering solver is presented to improve the convergence of the iterative solver for the linear system resulted by the integral quations. Its kernel idea is the selection of the main contribution of the matrix elements, which affect the matrix condition number the most. We employ the important part similar to the near-field to build the preconditioning matrix. A parameter delta is given to control the balance between the computational expense to get the preconditioner and the effectiveness of the preconditioner. A practical selection of the control parameter delta of the preconditioner is discussed, which indicates the preconditioner is effective in conjunction with a BiCGstab(l) solver.

The purpose of this paper is to introduce the work which has been carried out at NAG Ltd to update the iterative solvers for sparse systems of linear equations, both symmetric and unsymmetric, in the NAG Fortran 77 Library. Our current plans to extend this work and include it in our other numerical libraries in our range are also briefly mentioned. We have added to the Library the new Chapter F11, entirely dedicated to sparse linear algebra. At Mark 17, the F11 Chapter includes sparse iterative solvers, preconditioners, utilities and black-box routines for sparse symmetric (both positive-definite and indefinite) linear systems. Mark 18 will add solvers, preconditioners, utilities and black-boxes for sparse unsymmetric systems: the development of these has already been completed.

We consider a two-echelon, continuous review inventory system under Poisson demand and a one-for-one replenishment policy. Demand is lost if no items are available at the local warehouse, the central depot, or in the pipeline in between. We give a simple, fast and accurate approach to approximate

We present a probabilistic model of events in continuous time in which each event triggers a Poisson process of successor events. The ensemble of observed events is thereby modeled as a superposition of Poisson processes. Efficient inference is feasible under this model with an EM algorithm. Moreover, the EM algorithm can be implemented as a distributed algorithm, permitting the model to be applied to very large datasets. We apply these techniques to the modeling of Twitter messages and the revision history of Wikipedia.

Poisson׳s ratio of fibrous soft tissues is analyzed in this paper on the basis of constitutive models and experimental data. Three different up-to-date constitutive models accounting for the dispersion of fibre orientations are analyzed. Their predictions of the anisotropic Poisson׳s ratios are investigated under finite strain conditions together with the effects of specific orientation distribution functions and of other parameters. The applied constitutive models predict the tendency to lower (or even negative) out-of-plane Poisson׳s ratio. New experimental data of porcine arterial layer under uniaxial tension in orthogonal directions are also presented and compared with the theoretical predictions and other literature data. The results point out the typical features of recent constitutive models with fibres concentrated in circumferential-axial plane of arterial layers and their potential inconsistence with some experimental data. The volumetric (in)compressibility of arterial tissues is also discussed as an eventual and significant factor influencing this inconsistency.

Full Text Available Various linear or nonlinear electronic circuits can be described bythe set of ordinary differential equations (ODEs. The ordinarydifferential equations can be solved in the MATLAB environment inanalytical (symbolic toolbox or numerical way. The set of nonlinearODEs with high complexity can be usually solved only by use ofnumerical integrator (solver. The modification of ode23 MATLABnumerical solver has been suggested in this article for the applicationin solution of some special cases of ODEs. The main feature of thismodification is that the solution is found at every prescribed point,in which the special behavior of system is anticipated. Theextrapolation of solution is not allowed in those points.

vZ is a part of the SMT solver Z3. It allows users to pose and solve optimization problems modulo theories. Many SMT applications use models to provide satisfying assignments, and a growing number of these build on top of Z3 to get optimal assignments with respect to objective functions. vZ provi...

We prove that the generalized Poisson distribution GP(theta, eta) (eta > or = 0) is a mixture of Poisson distributions; this is a new property for a distribution which is the topic of the book by Consul (1989). Because we find that the fits to count data of the generalized Poisson and negative binomial distributions are often similar, to understand their differences, we compare the probability mass functions and skewnesses of the generalized Poisson and negative binomial distributions with the first two moments fixed. They have slight differences in many situations, but their zero-inflated distributions, with masses at zero, means and variances fixed, can differ more. These probabilistic comparisons are helpful in selecting a better fitting distribution for modelling count data with long right tails. Through a real example of count data with large zero fraction, we illustrate how the generalized Poisson and negative binomial distributions as well as their zero-inflated distributions can be discriminated.

Model-based reconstruction of electrical brain activity from electro-encephalographic measurements is of growing importance in neurology and neurosurgery. Algorithms for this task involve the solution of a 3D Poisson problem on a realistic head geometry obtained from medical imaging. In the model, several compartments with different conductivities have to be distinguished, leading to a problem with jumping coefficients. Furthermore, the Poisson problem needs to be solved repeatedly for different source contributions. Thus efficient solvers for this subtask are required. Experience with different iterative solvers is reported, i.e. successive over-relaxation, (preconditioned) conjugate gradients and algebraic multigrid, for a discretisation based on cell-centred finite differences. It was found that: first, the multigrid-based solver performed the task 1.8-3.5 times faster, depending on the platform, than the second-best contender; secondly, there was no need to introduce a reference potential that forced a unique solution; and, thirdly, neither the grid- nor matrix-based implementation of the solvers consistently gave a smaller run time.

This paper describes performance bounds for compressed sensing (CS) where the underlying sparse or compressible (sparsely approximable) signal is a vector of nonnegative intensities whose measurements are corrupted by Poisson noise. In this setting, standard CS techniques cannot be applied directly for several reasons. First, the usual signal-independent and/or bounded noise models do not apply to Poisson noise, which is non-additive and signal-dependent. Second, the CS matrices typically considered are not feasible in real optical systems because they do not adhere to important constraints, such as nonnegativity and photon flux preservation. Third, the typical $\\ell_2$--$\\ell_1$ minimization leads to overfitting in the high-intensity regions and oversmoothing in the low-intensity areas. In this paper, we describe how a feasible positivity- and flux-preserving sensing matrix can be constructed, and then analyze the performance of a CS reconstruction approach for Poisson data that minimizes an objective functi...

Paretian Poisson processes are a mathematical model of random fractal populations governed by Paretian power law tail statistics, and connect together and underlie elemental issues in statistical physics. Considering Paretian Poisson processes to represent the wealth of individuals in human populations, we explore their oligarchic structure via the analysis of the following random ratios: the aggregate wealth of the oligarchs ranked from m+1 to n, measured relative to the wealth of the m-th oligarch (n> m). A mean analysis and a stochastic-limit analysis (as n→∞) of these ratios are conducted. We obtain closed-form results which turn out to be highly contingent on the fractal exponent of the Paretian Poisson process considered.

In this paper we introduce the space-fractional Poisson process whose state probabilities $p_k^\\alpha(t)$, $t>0$, $\\alpha \\in (0,1]$, are governed by the equations $(\\mathrm d/\\mathrm dt)p_k(t) = -\\lambda^\\alpha (1-B)p_k^\\alpha(t)$, where $(1-B)^\\alpha$ is the fractional difference operator found in the study of time series analysis. We explicitly obtain the distributions $p_k^\\alpha(t)$, the probability generating functions $G_\\alpha(u,t)$, which are also expressed as distributions of the minimum of i.i.d.\\ uniform random variables. The comparison with the time-fractional Poisson process is investigated and finally, we arrive at the more general space-time fractional Poisson process of which we give the explicit distribution.

Let the nodes of a Poisson point process move independently in $\\R^d$ according to Brownian motions. We study the isolation time for a target particle that is placed at the origin, namely how long it takes until there is no node of the Poisson point process within distance $r$ of it. We obtain asymptotics for the tail probability which are tight up to constants in the exponent in dimension $d\\geq 3$ and tight up to logarithmic factors in the exponent for dimensions $d=1,2$.

We propose an image deconvolution algorithm when the data is contaminated by Poisson noise. The image to restore is assumed to be sparsely represented in a dictionary of waveforms such as the wavelet or curvelet transform. Our key innovations are: First, we handle the Poisson noise properly by using the Anscombe variance stabilizing transform leading to a non-linear degradation equation with additive Gaussian noise. Second, the deconvolution problem is formulated as the minimization of a convex functional with a data-fidelity term reflecting the noise properties, and a non-smooth sparsity-promoting penalties over the image representation coefficients (e.g. l1-norm). Third, a fast iterative backward-forward splitting algorithm is proposed to solve the minimization problem. We derive existence and uniqueness conditions of the solution, and establish convergence of the iterative algorithm. Experimental results are carried out to show the striking benefits gained from taking into account the Poisson statistics of...

A new Newton-Raphson method based preconditioner for Krylov type linear equation solvers for GPGPU is developed, and the performance is investigated. Conventional preconditioners improve the convergence of Krylov type solvers, and perform well on CPUs. However, they do not perform well on GPGPUs, because of the complexity of implementing powerful preconditioners. The developed preconditioner is based on the BFGS Hessian matrix approximation technique, which is well known as a robust and fast nonlinear equation solver. Because the Hessian matrix in the BFGS represents the coefficient matrix of a system of linear equations in some sense, the approximated Hessian matrix can be a preconditioner. On the other hand, BFGS is required to store dense matrices and to invert them, which should be avoided on modern computers and supercomputers. To overcome these disadvantages, we therefore introduce a limited memory BFGS, which requires less memory space and less computational effort than the BFGS. In addition, a limited memory BFGS can be implemented with BLAS libraries, which are well optimized for target architectures. There are advantages and disadvantages to the Hessian matrix approximation becoming better as the Krylov solver iteration continues. The preconditioning matrix varies through Krylov solver iterations, and only flexible Krylov solvers can work well with the developed preconditioner. The GCR method, which is a flexible Krylov solver, is employed because of the prevalence of GCR as a Krylov solver with a variable preconditioner. As a result of the performance investigation, the new preconditioner indicates the following benefits: (1) The new preconditioner is robust; i.e., it converges while conventional preconditioners (the diagonal scaling, and the SSOR preconditioners) fail. (2) In the best case scenarios, it is over 10 times faster than conventional preconditioners on a CPU. (3) Because it requries only simple operations, it performs well on a GPGPU. In

We present a framework using the Quantized Tensor Train (QTT) decomposition to accurately and efficiently solve volume and boundary integral equations in three dimensions. We describe how the QTT decomposition can be used as a hierarchical compression and inversion scheme for matrices arising from the discretization of integral equations. For a broad range of problems, computational and storage costs of the inversion scheme are extremely modest O (log ⁡ N) and once the inverse is computed, it can be applied in O (Nlog ⁡ N) . We analyze the QTT ranks for hierarchically low rank matrices and discuss its relationship to commonly used hierarchical compression techniques such as FMM and HSS. We prove that the QTT ranks are bounded for translation-invariant systems and argue that this behavior extends to non-translation invariant volume and boundary integrals. For volume integrals, the QTT decomposition provides an efficient direct solver requiring significantly less memory compared to other fast direct solvers. We present results demonstrating the remarkable performance of the QTT-based solver when applied to both translation and non-translation invariant volume integrals in 3D. For boundary integral equations, we demonstrate that using a QTT decomposition to construct preconditioners for a Krylov subspace method leads to an efficient and robust solver with a small memory footprint. We test the QTT preconditioners in the iterative solution of an exterior elliptic boundary value problem (Laplace) formulated as a boundary integral equation in complex, multiply connected geometries.

Aleph models continuum electrostatic and steady and transient thermal fields using a finite-element method. Much work has gone into expanding the core solver capability to support enriched modeling consisting of multiple interacting fields, special boundary conditions and two-way interfacial coupling with particles modeled using Aleph's complementary particle-in-cell capability. This report provides quantitative evidence for correct implementation of Aleph's field solver via order- of-convergence assessments on a collection of problems of increasing complexity. It is intended to provide Aleph with a pedigree and to establish a basis for confidence in results for more challenging problems important to Sandia's mission that Aleph was specifically designed to address.

Quantified constraint satisfaction problems (QCSPs) are an extension to constraint satisfaction problems (CSPs) with both universal quantifiers and existential quantifiers.In this paper we apply variable ordering heuristics and integrate standard dependency schemes in QCSP solvers.The technique can help to decide the next variable to be assigned in QCSP solving.We also introduce a new factor into the variable ordering heuristics:a variable's dep is the number of variables depending on it.This factor represents the probability of getting more candidates for the next variable to be assigned.Experimental results show that variable ordering heuristics with standard dependency schemes and the new factor dep can improve the performance of QCSP solvers.

An implicit solver for compressible flows using Bi-CGSTAB method is proposed. The Euler equations are discretized with the delta-form by the finite volume method on the cell-centered triangular unstructured meshes. The numerical flux is calculated by Roe's upwind scheme. The linearized simultaneous equations with the irregular nonsymmetric sparse matrix are solved by the Bi-CGSTAB method with the preconditioner of incomplete LU factorization. This method is also vectorized by the multi-colored ordering. Although the solver requires more computational memory, it shows faster and more robust convergence than the other conventional methods: three-stage Runge-Kutta method, point Gauss-Seidel method, and Jacobi method for two-dimensional inviscid steady flows.

The numerical solution of high dimensional Vlasov equation is usually performed by particle-in-cell (PIC) methods. However, due to the well-known numerical noise, it is challenging to use PIC methods to get a precise description of the distribution function in phase space. To control the numerical error, we introduce an adaptive phase-space remapping which regularizes the particle distribution by periodically reconstructing the distribution function on a hierarchy of phase-space grids with high-order interpolations. The positivity of the distribution function can be preserved by using a local redistribution technique. The method has been successfully applied to a set of classical plasma problems in one dimension. In this paper, we present the algorithm for the two dimensional Vlasov-Poisson equations. An efficient Poissonsolver with infinite domain boundary conditions is used. The parallel scalability of the algorithm on massively parallel computers will be discussed.

This chapter is an attempt to present a mathematical theory of compound fractional Poisson processes. The chapter begins with the characterization of a well-known L\\'evy process: The compound Poisson process. The semi-Markov extension of the compound Poisson process naturally leads to the compound fractional Poisson process, where the Poisson counting process is replaced by the Mittag-Leffler counting process also known as fractional Poisson process. This process is no longer Markovian and L\\'evy. However, several analytical results are available and some of them are discussed here. The functional limit of the compound Poisson process is an $\\alpha$-stable L\\'evy process, whereas in the case of the compound fractional Poisson process, one gets an $\\alpha$-stable L\\'evy process subordinated to the fractional Poisson process.

Full Text Available The solution of chemical kinetics is one of the most computationally intensivetasks in atmospheric chemical transport simulations. Due to the stiff nature of the system,implicit time stepping algorithms which repeatedly solve linear systems of equations arenecessary. This paper reviews the issues and challenges associated with the construction ofefficient chemical solvers, discusses several families of algorithms, presents strategies forincreasing computational efficiency, and gives insight into implementing chemical solverson accelerated computer architectures.

Full Text Available We give a detailed description of a dynamical system which enjoys a Poisson-Lie symmetry with two non-isomorphic dual groups. The system is obtained by taking the q → ∞ limit of the q-deformed WZW model and the understanding of its symmetry structure results in uncovering an interesting duality of its exchange relations.

We establish an optimal transportation inequality for the Poisson measure on the configuration space. Furthermore, under the Dobrushin uniqueness condition, we obtain a sharp transportation inequality for the Gibbs measure on $\\mathbb{N}^{\\Lambda}$ or the continuum Gibbs measure on the configuration space.

We present versions of several classical results on harmonic functions and Poisson boundaries in the setting of locally compact quantum groups $\\mathbb{G}$. In particular, the Choquet-Deny theorem holds for compact quantum groups; also, the result of Kaimanovich-Vershik and Rosenblatt, which characterizes group amenability in terms of harmonic functions, answering a conjecture by Furstenberg, admits a non-commutative analogue in the separable case. We also explore the relation between classical and quantum Poisson boundaries by investigating the spectrum of the quantum group. We apply this machinery to find a concrete realization of the Poisson boundaries of the compact quantum group $SU_{q}(2)$ arising from measures on its spectrum. We further show that the Poisson boundary of the natural Markov operator extension of the convolution action of a quantum probability measure $\\mu$ on $L_\\infty(\\mathbb{G})$ to $B(L_2(\\mathbb{G}))$, as introduced and studied - for general completely bounded multipliers on $L_1(\\m...

Full Text Available On their journey across large land masses, water molecules experience a number of precipitation-evaporation cycles (recycling events. We derive analytically the frequency distributions of recycling events for the water molecules contained in a given air parcel. Given the validity of certain simplifying assumptions, continental moisture recycling is shown to develop either into a Poisson distribution or a geometric distribution. We distinguish two cases: in case (A recycling events are counted since the water molecules were last advected across the ocean-land boundary. In case (B recycling events are counted since the water molecules were last evaporated from the ocean. For case B we show by means of a simple scale analysis that, given the conditions on Earth, realistic frequency distributions may be regarded as a mixture of a Poisson distribution and a geometric distribution. By contrast, in case A the Poisson distribution generally appears as a reasonable approximation. This conclusion is consistent with the simulation results of an earlier study where an atmospheric general circulation model equipped with water vapor tracers was used. Our results demonstrate that continental moisture recycling can be interpreted as a Poisson process.

The construction of the Bayesian credible (confidence) interval for a Poisson observable including both the signal and background with and without systematic uncertainties is presented.Introducing the conditional probability satisfying the requirement of the background not larger than the observed events to construct the Bayesian credible interval is also discussed.A Fortran routine,BPOCI,has been developed to implement the calculation.

are identified, and where we simulate backwards and forwards in order to obtain the thinned process. In the case of a Cox process, a simple independent thinning technique is proposed. In both cases, the thinning results in a Poisson process if and only if the true Papangelou conditional intensity is used, and...

, and where one simulates backwards and forwards in order to obtain the thinned process. In the case of a Cox process, a simple independent thinning technique is proposed. In both cases, the thinning results in a Poisson process if and only if the true Papangelou conditional intensity is used, and thus can...

We address the problem of the joint statistical inference of phylogenetic trees and multiple sequence alignments from unaligned molecular sequences. This problem is generally formulated in terms of string-valued evolutionary processes along the branches of a phylogenetic tree. The classic evolutionary process, the TKF91 model [Thorne JL, Kishino H, Felsenstein J (1991) J Mol Evol 33(2):114-124] is a continuous-time Markov chain model composed of insertion, deletion, and substitution events. Unfortunately, this model gives rise to an intractable computational problem: The computation of the marginal likelihood under the TKF91 model is exponential in the number of taxa. In this work, we present a stochastic process, the Poisson Indel Process (PIP), in which the complexity of this computation is reduced to linear. The Poisson Indel Process is closely related to the TKF91 model, differing only in its treatment of insertions, but it has a global characterization as a Poisson process on the phylogeny. Standard results for Poisson processes allow key computations to be decoupled, which yields the favorable computational profile of inference under the PIP model. We present illustrative experiments in which Bayesian inference under the PIP model is compared with separate inference of phylogenies and alignments.

In this article we determine the Laplace transforms of the main boundary functionals of the oscillating compound Poisson process. These are the first passage time of the level, the joint distribution of the first exit time from the interval and the value of the overshoot through the boundary. Under certain conditions we establish the asymptotic behaviour of the mentioned functionals.

We present a multigrid solver for the exponential fitting method. The solver is applied to the current continuity equations of semiconductor device simulation in two dimensions. The exponential fitting method is based on a mixed finite element discretization using the lowest-order Raviart-Thomas triangular element. This discretization method yields a good approximation of front layers and guarantees current conservation. The corresponding stiffness matrix is an M-matrix. 'Standard' multigrid solvers, however, cannot be applied to the resulting system, as this is dominated by an unsymmetric part, which is due to the presence of strong convection in part of the domain. To overcome this difficulty, we explore the connection between Raviart-Thomas mixed methods and the nonconforming Crouzeix-Raviart finite element discretization. In this way we can construct nonstandard prolongation and restriction operators using easily computable weighted L(exp 2)-projections based on suitable quadrature rules and the upwind effects of the discretization. The resulting multigrid algorithm shows very good results, even for real-world problems and for locally refined grids.

We have developed a new pressure-correction method for simulating incompressible two-fluid flows with large density and viscosity ratios. The method's main advantage is that the variable coefficient Poisson equation that arises in solving the incompressible Navier-Stokes equations for two-fluid flows is reduced to a constant coefficient equation, which can be solved with an FFT-based, fastPoissonsolver. This reduction is achieved by splitting the variable density pressure gradient term in the governing equations. The validity of this splitting is demonstrated from our numerical tests, and it is explained from a physical viewpoint. In this paper, the new pressure-correction method is coupled with a mass-conserving volume-of-fluid method to capture the motion of the interface between the two fluids but, in general, it could be coupled with other interface advection methods such as level-set, phase-field, or front-tracking. First, we verified the new pressure-correction method using the capillary wave test-case up to density and viscosity ratios of 10,000. Then, we validated the method by simulating the motion of a falling water droplet in air and comparing the droplet terminal velocity with an experimental value. Next, the method is shown to be second-order accurate in space and time independent of the VoF method, and it conserves mass, momentum, and kinetic energy in the inviscid limit. Also, we show that for solving the two-fluid Navier-Stokes equations, the method is 10-40 times faster than the standard pressure-correction method, which uses multigrid to solve the variable coefficient Poisson equation. Finally, we show that the method is capable of performing fully-resolved direct numerical simulation (DNS) of droplet-laden isotropic turbulence with thousands of droplets using a computational mesh of 10243 points.

In this paper, we show that the twisted Poincaré duality between Poisson homology and cohomology can be derived from the Serre invertible bimodule. This gives another definition of a unimodular Poisson algebra in terms of its Poisson Picard group. We also achieve twisted Poincaré duality for Hochschild (co)homology of Poisson bimodules using rigid dualizing complex. For a smooth Poisson affine variety with the trivial canonical bundle, we prove that its enveloping algebra is a Calabi-Yau algebra if the Poisson structure is unimodular.

In this note we show how to construct a homotopy BV-algebra on the algebra of differential forms over a higher Poisson manifold. The Lie derivative along the higher Poisson structure provides the generating operator.

In present paper the possibility of construction of continuous analogue of Poisson distribution with the search of bounds of confidence intervals for parameter of Poisson distribution is discussed and the results of numerical construction of confidence intervals are presented.

We extend the Poisson bracket from a Lie bracket of phase space functions to a Lie bracket of functions on the space of canonical histories and investigate the resulting algebras. Typically, such extensions define corresponding Lie algebras on the space of Lagrangian histories via pull back to a space of partial solutions. These are the same spaces of histories studied with regard to path integration and decoherence. Such spaces of histories are familiar from path integration and some studies of decoherence. For gauge systems, we extend both the canonical and reduced Poisson brackets to the full space of histories. We then comment on the use of such algebras in time reparameterization invariant systems and systems with a Gribov ambiguity, though our main goal is to introduce concepts and techniques for use in a companion paper.

We observe $n$ inhomogeneous Poisson processes with covariates and aim at estimating their intensities. To handle this problem, we assume that the intensity of each Poisson process is of the form $s (\\cdot, x)$ where $x$ is the covariate and where $s$ is an unknown function. We propose a model selection approach where the models are used to approximate the multivariate function $s$. We show that our estimator satisfies an oracle-type inequality under very weak assumptions both on the intensities and the models. By using an Hellinger-type loss, we establish non-asymptotic risk bounds and specify them under various kind of assumptions on the target function $s$ such as being smooth or composite. Besides, we show that our estimation procedure is robust with respect to these assumptions.

The question of whether flares occur as a Poisson process has important consequences for flare physics. Recently Lepreti et al. presented evidence for local departure from Poisson statistics in the Geostationary Operational Environmental Satellite (GOES) X-ray flare catalog. Here it is argued that this effect arises from a selection effect inherent in the soft X-ray observations; namely that the slow decay of enhanced flux following a large flare makes detection of subsequent flares less likely. It is also shown that the power-law tail of the GOES waiting-time distribution varies with the solar cycle. This counts against any intrinsic significance to the appearance of a power law, or to the value of its index.

Device design involving metals and dielectrics at nano-scales and optical frequencies calls for simulation tools capable of analyzing plasmonic interactions. To this end finite difference time domain (FDTD) and finite element methods have been used extensively. Since these methods require volumetric meshes, the discretization size should be very small to accurately resolve fast-decaying fields in the vicinity of metal/dielectric interfaces. This can be avoided using integral equation (IE) techniques that discretize only on the interfaces. Additionally, IE solvers implicitly enforce the radiation condition and consequently do not need (approximate) absorbing boundary conditions. Despite these advantages, IE solvers, especially in time domain, have not been used for analyzing plasmonic interactions.

We establish the stabilities and blowup results for the nonisentropic Euler-Poisson equations by the energy method. By analysing the second inertia, we show that the classical solutions of the system with attractive forces blow up in finite time in some special dimensions when the energy is negative. Moreover, we obtain the stabilities results for the system in the cases of attractive and repulsive forces.

On their journey across large land masses, water molecules experience a number of precipitation-evaporation cycles (recycling events). We derive analytically the frequency distributions of recycling events for the water molecules contained in a given air parcel. Given the validity of certain simplifying assumptions, continental moisture recycling is shown to develop either into a Poisson distribution or a geometric distribution. We distinguish two cases: in case (A) recycling events a...

On their journey over large land masses, water molecules experience a number of precipitation–evaporation cycles (recycling events). We derive analytically the frequency distributions of recycling events for the water molecules contained in a given air parcel. Given the validity of certain simplifying assumptions, the frequency distribution of recycling events is shown to develop either into a Poisson distribution or a geometric distribution. We distingu...

A specialized Echeloned Poisson Series Processor (EPSP) is proposed. It is a typical software for the implementation of analytical algorithms of Celestial Mechanics. EPSP is designed for manipulating long polynomial-trigonometric series with literal divisors. The coefficients of these echeloned series are the rational or floating-point numbers. The Keplerian processor and analytical generator of special celestial mechanics functions based on the EPSP are also developed.

A kinetic model is derived to study the successive movements of particles, described by a Poisson process, as well as their generation. The irreversible thermodynamics of this system is also studied from the kinetic model. This makes it possible to evaluate the differences between thermodynamical quantities computed exactly and up to second-order. Such differences determine the range of validity of the second-order approximation to extended irreversible thermodynamics.

A kinetic model is derived to study the successive movements of particles, described by a Poisson process, as well as their generation. The irreversible thermodynamics of this system is also studied from the kinetic model. This makes it possible to evaluate the differences between thermodynamical quantities computed exactly and up to second-order. Such differences determine the range of validity of the second-order approximation to extended irreversible thermodynamics.

Full Text Available An alternative form of hyper-Poisson distribution is introduced through its probability mass function and studies some of its important aspects such as mean, variance, expressions for its raw moments, factorial moments, probability generating function and recursion formulae for its probabilities, raw moments and factorial moments. The estimation of the parameters of the distribution by various methods are considered and illustrated using some real life data sets.

We discuss the verification of mathematical software solving polynomial systems symbolically by way of triangular decomposition. Standard verification techniques are highly resource consuming and apply only to polynomial systems which are easy to solve. We exhibit a new approach which manipulates constructible sets represented by regular systems. We provide comparative benchmarks of different verification procedures applied to four solvers on a large set of well-known polynomial systems. Our experimental results illustrate the high effi-ciency of our new approach. In particular, we are able to verify triangular decompositions of polynomial systems which are not easy to solve.

The process of numerical simulation consists of selection of some items: a mathematical model, a numerical scheme, the level of the computer, and post processing. From this point of view, recent numerical studies of viscous flows are described especially for the fluid engineering laboratories in the Chiba University. The examples of simulations are Mach reflection on a wedge using a kinetic model equation and a cylinder-plate juncture flow using incompressible Navier Stokes equation. Some attempts at graphic monitoring of fluid mechanical calculations are also shown for some combinations of computers with Computational Fluid Dynamics (CFD) solvers.

To upgrade the efficiency and stability of the successive substitution (SS) and Newton-Raphson (NR) schemes, the concept of input-output-controlled solvers (IOCS) is introduced. By employing the formal properties of the constrained version of the SS and NR schemes, the IOCS algorithm can handle indefiniteness of the system Jacobian, can maintain iterate monotonicity, and provide for separate control of load incrementation and iterate excursions, as well as having other features. To illustrate the algorithmic properties, the results for several benchmark examples are presented. These define the associated numerical efficiency and stability of the IOCS.

The paper contains a short description of the DPS system which is a computerized diagnostic problem solver. The system is under development of the Research Institute of Medical Bionics in Bratislava, Czechoslovakia. Its underlying philosophy yields from viewing the diagnostic process as process of cognitive problem solving. The implementation of the system is based on the methods of Artificial Intelligence and utilisation of production systems and frame theory should be noted in this context. Finally a list of program modules and their characterisation is presented.

Metaheuristics: Progress as Real Problem Solvers is a peer-reviewed volume of eighteen current, cutting-edge papers by leading researchers in the field. Included are an invited paper by F. Glover and G. Kochenberger, which discusses the concept of Metaheuristic agent processes, and a tutorial paper by M.G.C. Resende and C.C. Ribeiro discussing GRASP with path-relinking. Other papers discuss problem-solving approaches to timetabling, automated planograms, elevators, space allocation, shift design, cutting stock, flexible shop scheduling, colorectal cancer and cartography. A final group of methodology papers clarify various aspects of Metaheuristics from the computational view point.

This paper describes a new way to design and fabricate compliant micromechanisms and material structures with negative Poisson's ratio (NPR). The design of compliant mechanisms and material structures is accomplished in an automated way using a numerical topology optimization method, The procedure......, all in one two-step reactive ion etching (RIE) process. The components are tested using a probe placed on an x-y stage. This fast prototyping allows newly developed topologies to be fabricated and tested within the same day...

The nonlocal dielectric approach has led to new models and solvers for predicting electrostatics of proteins (or other biomolecules), but how to validate and compare them remains a challenge. To promote such a study, in this paper, two typical nonlocal dielectric models are revisited. Their analytical solutions are then found in the expressions of simple series for a dielectric sphere containing any number of point charges. As a special case, the analytical solution of the corresponding Poisson dielectric model is also derived in simple series, which significantly improves the well known Kirkwood's double series expansion. Furthermore, a convolution of one nonlocal dielectric solution with a commonly used nonlocal kernel function is obtained, along with the reaction parts of these local and nonlocal solutions. To turn these new series solutions into a valuable research tool, they are programed as a free fortran software package, which can input point charge data directly from a protein data bank file. Consequently, different validation tests can be quickly done on different proteins. Finally, a test example for a protein with 488 atomic charges is reported to demonstrate the differences between the local and nonlocal models as well as the importance of using the reaction parts to develop local and nonlocal dielectric solvers.

The nonlocal dielectric approach has led to new models and solvers for predicting electrostatics of proteins (or other biomolecules), but how to validate and compare them remains a challenge. To promote such a study, in this paper, two typical nonlocal dielectric models are revisited. Their analytical solutions are then found in the expressions of simple series for a dielectric sphere containing any number of point charges. As a special case, the analytical solution of the corresponding Poisson dielectric model is also derived in simple series, which significantly improves the well known Kirkwood's double series expansion. Furthermore, a convolution of one nonlocal dielectric solution with a commonly used nonlocal kernel function is obtained, along with the reaction parts of these local and nonlocal solutions. To turn these new series solutions into a valuable research tool, they are programed as a free fortran software package, which can input point charge data directly from a protein data bank file. Consequently, different validation tests can be quickly done on different proteins. Finally, a test example for a protein with 488 atomic charges is reported to demonstrate the differences between the local and nonlocal models as well as the importance of using the reaction parts to develop local and nonlocal dielectric solvers.

Full Text Available We study here different fractional versions of the compound Poisson process. The fractionality is introduced in the counting process representing the number of jumps as well as in the density of the jumps themselves. The corresponding distributions are obtained explicitly and proved to be solution of fractional equations of order less than one. Only in the final case treated in this paper, where the number of jumps is given by the fractional-difference Poisson process defined in Orsingher and Polito (2012, we have a fractional driving equation, with respect to the time argument, with order greater than one. Moreover, in this case, the compound Poisson process is Markovian and this is also true for the corresponding limiting process. All the processes considered here are proved to be compositions of continuous time random walks with stable processes (or inverse stable subordinators. These subordinating relationships hold, not only in the limit, but also in the finite domain. In some cases the densities satisfy master equations which are the fractional analogues of the well-known Kolmogorov one.

The induced two-dimensional topological N=1 supersymmetric sigma model on a differential Poisson manifold M presented in arXiv:1503.05625 is shown to be a special case of the induced Poisson sigma model on the bi-graded supermanifold T[0,1]M. The bi-degree comprises the standard N-valued target space degree, corresponding to the form degree on the worldsheet, and an additional Z-valued fermion number, corresponding to the degree in the differential graded algebra of forms on M. The N=1 supersymmetry stems from the compatibility between the (extended) differential Poisson bracket and the de Rham differential on M. The latter is mapped to a nilpotent vector field Q of bi-degree (0,1) on T*[1,0](T[0,1]M), and the covariant Hamiltonian action is Q-exact. New extended supersymmetries arise as inner derivatives along special bosonic Killing vectors on M that induce Killing supervector fields of bi-degree (0,-1) on T*[1,0](T[0,1]M).

We consider a class of point processes (pp), which we call {\\em sub-Poisson}; these are pp that can be directionally-convexly ($dcx$) dominated by some Poisson pp. The $dcx$ order has already been shown useful in comparing various point process characteristics, including Ripley's and correlation functions as well as shot-noise fields generated by pp, indicating in particular that smaller in the $dcx$ order processes exhibit more regularity (less clustering, less voids) in the repartition of their points. Using these results, in this paper we study the impact of the $dcx$ ordering of pp on the properties of two continuum percolation models, which have been proposed in the literature to address macroscopic connectivity properties of large wireless networks. As the first main result of this paper, we extend the classical result on the existence of phase transition in the percolation of the Gilbert's graph (called also the Boolean model), generated by a homogeneous Poisson pp, to the class of homogeneous sub-Pois...

In this paper we consider the relation between random sums and compositions of different processes. In particular, for independent Poisson processes N α ( t), N β ( t), t>0, we have that N_{α}(N_{β}(t)) stackrel{d}{=} sum_{j=1}^{N_{β}(t)} Xj, where the X j s are Poisson random variables. We present a series of similar cases, where the outer process is Poisson with different inner processes. We highlight generalisations of these results where the external process is infinitely divisible. A section of the paper concerns compositions of the form N_{α}(tauk^{ν}), ν∈(0,1], where tauk^{ν} is the inverse of the fractional Poisson process, and we show how these compositions can be represented as random sums. Furthermore we study compositions of the form Θ( N( t)), t>0, which can be represented as random products. The last section is devoted to studying continued fractions of Cauchy random variables with a Poisson number of levels. We evaluate the exact distribution and derive the scale parameter in terms of ratios of Fibonacci numbers.

The Poisson-Boltzmann equation models the electrostatic potential generated by fixed charges on a polarizable solute immersed in an ionic solution. This approach is often used in computational structural biology to estimate the electrostatic energetic component of the assembly of molecular biological systems. In the last decades, the amount of data concerning proteins and other biological macromolecules has remarkably increased. To fruitfully exploit these data, a huge computational power is needed as well as software tools capable of exploiting it. It is therefore necessary to move towards high performance computing and to develop proper parallel implementations of already existing and of novel algorithms. Nowadays, workstations can provide an amazing computational power: up to 10 TFLOPS on a single machine equipped with multiple CPUs and accelerators such as Intel Xeon Phi or GPU devices. The actual obstacle to the full exploitation of modern heterogeneous resources is efficient parallel coding and porting of software on such architectures. In this paper, we propose the implementation of a full Poisson-Boltzmann solver based on a finite-difference scheme using different and combined parallel schemes and in particular a mixed MPI-CUDA implementation. Results show great speedups when using the two schemes, achieving an 18.9x speedup using three GPUs. PMID:25013789

The Poisson-Boltzmann equation models the electrostatic potential generated by fixed charges on a polarizable solute immersed in an ionic solution. This approach is often used in computational structural biology to estimate the electrostatic energetic component of the assembly of molecular biological systems. In the last decades, the amount of data concerning proteins and other biological macromolecules has remarkably increased. To fruitfully exploit these data, a huge computational power is needed as well as software tools capable of exploiting it. It is therefore necessary to move towards high performance computing and to develop proper parallel implementations of already existing and of novel algorithms. Nowadays, workstations can provide an amazing computational power: up to 10 TFLOPS on a single machine equipped with multiple CPUs and accelerators such as Intel Xeon Phi or GPU devices. The actual obstacle to the full exploitation of modern heterogeneous resources is efficient parallel coding and porting of software on such architectures. In this paper, we propose the implementation of a full Poisson-Boltzmann solver based on a finite-difference scheme using different and combined parallel schemes and in particular a mixed MPI-CUDA implementation. Results show great speedups when using the two schemes, achieving an 18.9x speedup using three GPUs.

Full Text Available The Poisson-Boltzmann equation models the electrostatic potential generated by fixed charges on a polarizable solute immersed in an ionic solution. This approach is often used in computational structural biology to estimate the electrostatic energetic component of the assembly of molecular biological systems. In the last decades, the amount of data concerning proteins and other biological macromolecules has remarkably increased. To fruitfully exploit these data, a huge computational power is needed as well as software tools capable of exploiting it. It is therefore necessary to move towards high performance computing and to develop proper parallel implementations of already existing and of novel algorithms. Nowadays, workstations can provide an amazing computational power: up to 10 TFLOPS on a single machine equipped with multiple CPUs and accelerators such as Intel Xeon Phi or GPU devices. The actual obstacle to the full exploitation of modern heterogeneous resources is efficient parallel coding and porting of software on such architectures. In this paper, we propose the implementation of a full Poisson-Boltzmann solver based on a finite-difference scheme using different and combined parallel schemes and in particular a mixed MPI-CUDA implementation. Results show great speedups when using the two schemes, achieving an 18.9x speedup using three GPUs.

We propose a nonlocal Poisson-Fermi model for ionic solvent that includes ion size effects and polarization correlations among water molecules in the calculation of electrostatic potential. It includes the previous Poisson-Fermi models as special cases, and its solution is the convolution of a solution of the corresponding nonlocal Poisson dielectric model with a Yukawa-type kernel function. Moreover, the Fermi distribution is shown to be a set of optimal ionic concentration functions in the sense of minimizing an electrostatic potential free energy. Finally, numerical results are reported to show the difference between a Poisson-Fermi solution and a corresponding Poisson solution.

We propose a nonlocal Poisson-Fermi model for ionic solvent that includes ion size effects and polarization correlations among water molecules in the calculation of electrostatic potential. It includes the previous Poisson-Fermi models as special cases, and its solution is the convolution of a solution of the corresponding nonlocal Poisson dielectric model with a Yukawa-like kernel function. The Fermi distribution is shown to be a set of optimal ionic concentration functions in the sense of minimizing an electrostatic potential free energy. Numerical results are reported to show the difference between a Poisson-Fermi solution and a corresponding Poisson solution.

When attempting to compute unsteady, variable density flows at very small or zero Mach number using a standard finite volume compressible flow solver one faces at least the following difficulties: (i) Spatial pressure variations vanish as the Mach number M→0, but they do affect the velocity field at leading order; (ii) the resulting spatial homogeneity of the leading order pressure implies an elliptic divergence constraint for the energy flux; (iii) violations of this constraint crucially affect the transport of mass, preventing a code to properly advect even a constant density distribution. We overcome these difficulties through a new algorithm for constructing numerical fluxes in the context of multi-dimensional finite volume methods in conservation form. The construction of numerical fluxes involves: (1) An explicit upwind step yielding predictions for the nonlinear convective flux components. (2) A first correction step that introduces pressure gradients which guarantee compliance of the convective fluxes with a divergence constraint. This step requires the solution of a first Poisson-type equation. (3) A second projection step which provides the yet unknown (non-convective) pressure contribution to the total flux of momentum. This second projection requires the solution of another Poisson-type equation and yields the cell centered velocity field at the new time. This velocity field exactly satisfies a divergence constraint consistent with the asymptotic limit. Step (1) can be done by any standard finite volume compressible flow solver. The input to steps (2) and (3) involves solely the fluxes from step (1) and is independent of how these were obtained. Thus, our approach allows any such solver to be extended to compute variable density incompressible flows.

Identifying fast and robust numerical solvers is a critical issue that needs to be addressed in order to improve projections of polar ice sheets evolving in a changing climate. This work evaluates the impact of using advanced numerical solvers for transient ice-flow simulations conducted with the JPL-UCI Ice Sheet System Model (ISSM). We identify optimal numerical solvers by testing a broad suite of readily available solvers, ranging from direct sparse solvers to preconditioned iterative methods, on the commonly used Ice Sheet Model Intercomparison Project for Higher-Order ice sheet Models benchmark tests. Three types of analyses are considered: mass transport, horizontal stress balance, and incompressibility. The results of the fastest solvers for each analysis type are ranked based on their scalability across mesh size and basal boundary conditions. We find that the fastest iterative solvers are ˜ 1.5-100 times faster than the default direct solver used in ISSM, with speed-ups improving rapidly with increased mesh resolution. We provide a set of recommendations for users in search of efficient solvers to use for transient ice-flow simulations, enabling higher-resolution meshes and faster turnaround time. The end result will be improved transient simulations for short-term, highly resolved forward projections (10-100 year time scale) and also improved long-term paleo-reconstructions using higher-order representations of stresses in the ice. This analysis will also enable a new generation of comprehensive uncertainty quantification assessments of forward sea-level rise projections, which rely heavily on ensemble or sampling approaches that are inherently expensive.

Paretian Poisson processes are Poisson processes which are defined on the positive half-line, have maximal points, and are quantified by power-law intensities. Paretian Poisson processes are elemental in statistical physics, and are the bedrock of a host of power-law statistics ranging from Pareto's law to anomalous diffusion. In this paper we establish evenness-based fractal characterizations of Paretian Poisson processes. Considering an array of socioeconomic evenness-based measures of statistical heterogeneity, we show that: amongst the realm of Poisson processes which are defined on the positive half-line, and have maximal points, Paretian Poisson processes are the unique class of 'fractal processes' exhibiting scale-invariance. The results established in this paper are diametric to previous results asserting that the scale-invariance of Poisson processes-with respect to physical randomness-based measures of statistical heterogeneity-is characterized by exponential Poissonian intensities.

In this paper we consider the relation between random sums and compositions of different processes. In particular, for independent Poisson processes $N_\\alpha(t)$, $N_\\beta(t)$, $t>0$, we show that $N_\\alpha(N_\\beta(t)) \\overset{\\text{d}}{=} \\sum_{j=1}^{N_\\beta(t)} X_j$, where the $X_j$s are Poisson random variables. We present a series of similar cases, the most general of which is the one in which the outer process is Poisson and the inner one is a nonlinear fractional birth process. We highlight generalisations of these results where the external process is infinitely divisible. A section of the paper concerns compositions of the form $N_\\alpha(\\tau_k^\

We analyse the cosmic ray magnetohydrodynamic (CR MHD) equations to improve the numerical simulations. We propose to solve them in the fully conservation form, which is equivalent to the conventional CR MHD equations. In the fully conservation form, the CR energy equation is replaced with the CR `number' conservation, where the CR number density is defined as the three-fourths power of the CR energy density. The former contains an extra source term, while latter does not. An approximate Riemann solver is derived from the CR MHD equations in the fully conservation form. Based on the analysis, we propose a numerical scheme of which solutions satisfy the Rankine-Hugoniot relation at any shock. We demonstrate that it reproduces the Riemann solution derived by Pfrommer et al. for a 1D CR hydrodynamic shock tube problem. We compare the solution with those obtained by solving the CR energy equation. The latter solutions deviate from the Riemann solution seriously, when the CR pressure dominates over the gas pressure in the post-shocked gas. The former solutions converge to the Riemann solution and are of the second-order accuracy in space and time. Our numerical examples include an expansion of high-pressure sphere in a magnetized medium. Fast and slow shocks are sharply resolved in the example. We also discuss possible extension of the CR MHD equations to evaluate the average CR energy.

Count data often show overdispersion compared to the Poisson distribution. Overdispersion is typically modeled by a random effect for the mean, based on the gamma distribution, leading to the negative binomial distribution for the count. This paper considers a larger family of mixture distributions, including the inverse Gaussian mixture distribution. It is demonstrated that it gives a significantly better fit for a data set on the frequency of epileptic seizures. The same approach can be used to generate counting processes from Poisson processes, where the rate or the time is random. A random rate corresponds to variation between patients, whereas a random time corresponds to variation within patients.

This paper discusses the relationship between elastic wave velocities and physical properties of reservoir rocks. For sandstones, the elastic wave velocity decreases with increasing the porosity and the content of clay minerals. For rocks containing heavy oil, the P-wave velocity decreases with increasing the temperature. The P-wave velocity under dry condition is much more lower than that under water saturated condition. When there are a few percent of gas in pores against the water saturated condition, the P-wave velocity decreases rapidly. It is almost constant under the lower water saturation factor. The S-wave velocity is almost constant independent of the water saturation factor. Accordingly, the water saturation factor can not be estimated from the elastic wave velocity at the water saturation factor between 0% and 96%. The Poisson`s ratio also greatly decreases at the water saturation factor between 96% and 100%, but it is almost constant under the lower water saturation factor. The elastic wave velocity increases with increasing the pressure or increasing the depth. Since closure of cracks by pressure is inhibited due to high pore pressure, degree of increase in the elastic wave velocity is reduced. 14 refs., 6 figs.

This paper presents an interactive MINLP solver that is particularly suitable for solution of process synthesis, design and analysis problems. The interactive MINLP solver is based on the decomposition based MINLP algorithms, where a NLP sub-problem is solved in the innerloop and a MILP master...

by a Krylov subspace iterative solver. By choosing convergence criteria for the iterative solver that are strongly related to the optimization objective and to the design sensitivities, it is possible to terminate the iterative solution of the nested equations earlier compared to traditional convergence...

This talk will focus on practical experiences with iterative linear solver algorithms used in conjunction with Amoco Production Company`s Falcon oil reservoir simulation code. The goal of this study is to determine the best linear solver algorithms for these types of problems. The results of numerical experiments will be presented.

A remarkable theoretical prediction for a crystalline (polymerized) surface is that its Poisson ratio (\\sigma) is negative. Using a large scale Monte Carlo simulation of a simple model of such surfaces we show that this is indeed true. The precise numerical value we find is (\\sigma \\simeq -0.32) on a (128^2) lattice at bending rigidity (kappa = 1.1). This is in excellent agreement with the prediction (\\sigma = -1/3) following from the self-consistent screening approximation of Le Doussal and ...

This is a review aimed at a physics audience on the relation between Poisson sigma models on surfaces with boundary and deformation quantization. These models are topological open string theories. In the classical Hamiltonian approach, we describe the reduced phase space and its structures (symplectic groupoid), explaining in particular the classical origin of the non-commutativity of the string end-point coordinates. We also review the perturbative Lagrangian approach and its connection with Kontsevich's star product. Finally we comment on the relation between the two approaches.

Let Pi and Gamma be homogeneous Poisson point processes on a fixed set of finite volume. We prove a necessary and sufficient condition on the two intensities for the existence of a coupling of Pi and Gamma such that Gamma is a deterministic function of Pi, and all points of Gamma are points of Pi. The condition exhibits a surprising lack of monotonicity. However, in the limit of large intensities, the coupling exists if and only if the expected number of points is at least one greater in Pi than in Gamma.

This book describes algorithmic methods and parallelization techniques to design a parallel sparse direct solver which is specifically targeted at integrated circuit simulation problems. The authors describe a complete flow and detailed parallel algorithms of the sparse direct solver. They also show how to improve the performance by simple but effective numerical techniques. The sparse direct solver techniques described can be applied to any SPICE-like integrated circuit simulator and have been proven to be high-performance in actual circuit simulation. Readers will benefit from the state-of-the-art parallel integrated circuit simulation techniques described in this book, especially the latest parallel sparse matrix solution techniques. · Introduces complicated algorithms of sparse linear solvers, using concise principles and simple examples, without complex theory or lengthy derivations; · Describes a parallel sparse direct solver that can be adopted to accelerate any SPICE-like integrated circuit simulato...

In this project, we investigated adaptive, parallel, and multilevel methods for numerical modeling of various real-world applications, including Magnetohydrodynamics (MHD), complex fluids, Electromagnetism, Navier-Stokes equations, and reservoir simulation. First, we have designed improved mathematical models and numerical discretizaitons for viscoelastic fluids and MHD. Second, we have derived new a posteriori error estimators and extended the applicability of adaptivity to various problems. Third, we have developed multilevel solvers for solving scalar partial differential equations (PDEs) as well as coupled systems of PDEs, especially on unstructured grids. Moreover, we have integrated the study between adaptive method and multilevel methods, and made significant efforts and advances in adaptive multilevel methods of the multi-physics problems.

This work arises from the introduction of a parallel iterative solver to a large structural analysis finite element code. The code is called FEX and it was developed at Hitachi`s Mechanical Engineering Laboratory. The FEX package can deal with a large range of structural analysis problems using a large number of finite element techniques. FEX can solve either stress or thermal analysis problems of a range of different types from plane stress to a full three-dimensional model. These problems can consist of a number of different materials which can be modelled by a range of material models. The structure being modelled can have the load applied at either a point or a surface, or by a pressure, a centrifugal force or just gravity. Alternatively a thermal load can be applied with a given initial temperature. The displacement of the structure can be constrained by having a fixed boundary or by prescribing the displacement at a boundary.

Full Text Available A Navier-Stokes equations solver is parallelized to run on a cluster of computers using the domain decomposition method. Two approaches of communication and computation are investigated, namely, synchronous and asynchronous methods. Asynchronous communication between subdomains is not commonly used in CFD codes; however, it has a potential to alleviate scaling bottlenecks incurred due to processors having to wait for each other at designated synchronization points. A common way to avoid this idle time is to overlap asynchronous communication with computation. For this to work, however, there must be something useful and independent a processor can do while waiting for messages to arrive. We investigate an alternative approach of computation, namely, conducting asynchronous iterations to improve local subdomain solution while communication is in progress. An in-house CFD code is parallelized using message passing interface (MPI, and scalability tests are conducted that suggest asynchronous iterations are a viable way of parallelizing CFD code.

We study some simple generalizations of the Poisson-Mehler summation formula (PM). In particular we exploit farther, the recently obtained equality {\\gamma}_{m,n}(x,y|t,q) = {\\gamma}_{0,0}(x,y|t,q)Q_{m,n}(x,y|t,q) where {\\gamma}_{m,n}(x,y|t,q) = \\Sigma_{i\\geq0}((t^{i})/([i]_{q}!))H_{i+n}(x|q)H_{m+i}(y|q), {H_{n}(x|q)}_{n\\geq-1} are the so called q-Hermite polynomials and {Q_{m,n}(x,y|t,q)}_{n,m\\geq0} are certain polynomials in x,y of order m+n being rational functions in t and q. We study properties of polynomials Q_{m,n}(x,y|t,q) expressing them with the help the so called Al-Salam--Chihara (ASC) polynomials and using them in expansion of the reciprocal of the right hand side of the Poisson-Mehler formula. We prove also some similar in nature equalities like e.g. the following \\Sigma_{i\\geq0}((t^{i})/([i]_{q}!))H_{n+i}(x|q) = H_{n}(x|t,q)\\Sigma_{i\\geq0}((t^{i})/([i]_{q}!))H_{i}(x|q), where H_{n}(x|t,q) is the so called big q-Hermite polynomial. We prove similar equalities involving big q-Hermite and ASC poly...

Full Text Available A Markov Modulated Poisson Process (MMPP M(t defined on a Markov chain J(t is a pure jump process where jumps of M(t occur according to a Poisson process with intensity λi whenever the Markov chain J(t is in state i. M(t is called strongly renewal (SR if M(t is a renewal process for an arbitrary initial probability vector of J(t with full support on P={i:λi>0}. M(t is called weakly renewal (WR if there exists an initial probability vector of J(t such that the resulting MMPP is a renewal process. The purpose of this paper is to develop general characterization theorems for the class SR and some sufficiency theorems for the class WR in terms of the first passage times of the bivariate Markov chain [J(t,M(t]. Relevance to the lumpability of J(t is also studied.

A marching on in time (MOT) scheme for solving the Poggio-Miller-Chan-Harrington-Wu-Tsai (PMCHWT) surface integral equation on plasmonic nanostructures is described. The proposed scheme calls for temporal convolutions of the permittivity and Green function of the plasmonic medium with the temporal basis function. Time domain samples of the permittivity and the Green function required by these convolutions are computed using a fast relaxed vector fitting (FRVF) algorithm. Numerical results demonstrate the accuracy and applicability of the proposed MOT-PMCHWT solver.

Full Text Available We describe two methods and provide C programs for generating discrete random variables with functions that are simple and fast, averaging ten times as fast as published methods and more than five times as fast as the fastest of those. We provide general procedures for implementing the two methods, as well as specific procedures for three of the most important discrete distributions: Poisson, binomial and hypergeometric.

Full Text Available Poisson regression was used to analyze the count data which Poisson distributed. Poisson regression analysis requires state equidispersion, in which the mean value of the response variable is equal to the value of the variance. However, there are deviations in which the value of the response variable variance is greater than the mean. This is called overdispersion. If overdispersion happens and Poisson Regression analysis is being used, then underestimated standard errors will be obtained. Negative Binomial Regression can handle overdispersion because it contains a dispersion parameter. From the simulation data which experienced overdispersion in the Poisson Regression model it was found that the Negative Binomial Regression was better than the Poisson Regression model.

Full Text Available Poisson regression was used to analyze the count data which Poisson distributed. Poisson regression analysis requires state equidispersion, in which the mean value of the response variable is equal to the value of the variance. However, there are deviations in which the value of the response variable variance is greater than the mean. This is called overdispersion. If overdispersion happens and Poisson Regression analysis is being used, then underestimated standard errors will be obtained. Negative Binomial Regression can handle overdispersion because it contains a dispersion parameter. From the simulation data which experienced overdispersion in the Poisson Regression model it was found that the Negative Binomial Regression was better than the Poisson Regression model.

We have developed and implemented a general formalism for fast numerical solution of time-independent linear partial differential equations as well as integral equations through the application of numerically separable integral operators in d ≥ 1 dimensions using the non-standard (NS) form. The proposed formalism is universal, compact and oriented towards the practical implementation into a working code using multiwavelets. The formalism is applied to the case of Poisson and bound-state Helmholtz operators in d = 3. Our algorithms are fully adaptive in the sense that the grid supporting each function is obtained on the fly while the function is being computed. In particular, when the function g = O f is obtained by applying an integral operator O, the corresponding grid is not obtained by transferring the grid from the input function f. This aspect has significant implications that will be discussed in the numerical section. The operator kernels are represented in a separated form with finite but arbitrary precision using Gaussian functions. Such a representation combined with the NS form allows us to build a sparse, banded representation of Green's operator kernel. We have implemented a code for the application of such operators in a separated NS form to a multivariate function in a finite but, in principle, arbitrary number of dimensions. The error of the method is controlled, while the low complexity of the numerical algorithm is kept. The implemented code explicitly computes all the 22d components of the d-dimensional operator. Our algorithms are described in detail in the paper through pseudo-code examples. The final goal of our work is to be able to apply this method to build a fast and accurate Kohn-Sham solver for density functional theory.

in fewer than 5 or so iterations. We employ a fast convex quadratic programming solver to carry out the iterations, which is more than fast enough to run in real-time. We demonstrate our method on a realistic model, with a full year simulation, using real historical data. These simulations show substantial...

When developing linear programming models, issues such as budget limitations, customer requirements, or licensing may preclude the use of commercial linear programming solvers. In such cases, one option is to use an open-source linear programming solver. A survey of linear programming tools was conducted to identify potential open-source solvers. From this survey, four open-source solvers were tested using a collection of linear programming test problems and the results were compared to IBM ILOG CPLEX Optimizer (CPLEX) [1], an industry standard. The solvers considered were: COIN-OR Linear Programming (CLP) [2], [3], GNU Linear Programming Kit (GLPK) [4], lp_solve [5] and Modular In-core Nonlinear Optimization System (MINOS) [6]. As no open-source solver outperforms CPLEX, this study demonstrates the power of commercial linear programming software. CLP was found to be the top performing open-source solver considered in terms of capability and speed. GLPK also performed well but cannot match the speed of CLP or CPLEX. lp_solve and MINOS were considerably slower and encountered issues when solving several test problems.

We formulate Yang-Mills theory in terms of the large-N limit, viewed as a classical limit, of gauge-invariant dynamical variables, which are closely related to Wilson loops, via deformation quantization. We obtain a Poisson algebra of these dynamical variables corresponding to normal-ordered quantum (at a finite value of ℏ) operators. Comparing with a Poisson algebra one of us introduced in the past for Weyl-ordered quantum operators, we find, using ideas closely related to topological graph theory, that these two Poisson algebras are, roughly speaking, the same. More precisely speaking, there exists an invertible Poisson morphism between them.

We consider a Poisson process $\\eta$ on an arbitrary measurable space with an arbitrary sigma-finite intensity measure. We establish an explicit Fock space representation of square integrable functions of $\\eta$. As a consequence we identify explicitly, in terms of iterated difference operators, the integrands in the Wiener-Ito chaos expansion. We apply these results to extend well-known variance inequalities for homogeneous Poisson processes on the line to the general Poisson case. The Poincare inequality is a special case. Further applications are covariance identities for Poisson processes on (strictly) ordered spaces and Harris-FKG-inequalities for monotone functions of $\\eta$.

The fractional Poisson process is a renewal process with Mittag-Leffler waiting times. Its distributions solve a time-fractional analogue of the Kolmogorov forward equation for a Poisson process. This paper shows that a traditional Poisson process, with the time variable replaced by an independent inverse stable subordinator, is also a fractional Poisson process. This result unifies the two main approaches in the stochastic theory of time-fractional diffusion equations. The equivalence extends to a broad class of renewal processes that include models for tempered fractional diffusion, and distributed-order (e.g., ultraslow) fractional diffusion.

Full Text Available This paper intends to generate the approximate Voronoi diagram in the geodesic metric for some unbiased samples selected from original points. The mesh model of seeds is then constructed on basis of the Voronoi diagram. Rather than constructing the Voronoi diagram for all original points, the proposed strategy is to run around the obstacle that the geodesic distances among neighboring points are sensitive to nearest neighbor definition. It is obvious that the reconstructed model is the level of detail of original points. Hence, our main motivation is to deal with the redundant scattered points. In implementation, Poisson disk sampling is taken to select seeds and helps to produce the Voronoi diagram. Adaptive reconstructions can be achieved by slightly changing the uniform strategy in selecting seeds. Behaviors of this method are investigated and accuracy evaluations are done. Experimental results show the proposed method is reliable and effective.

Starting with the well-defined product of quantum fields at two spacetime points, we explore an associated Poisson structure for classical field theories within the deformation quantization formalism. We realize that the induced star-product is naturally related to the standard Moyal product through the causal Green functions connecting points in the space of classical solutions to the equations of motion. Our results resemble the Peierls-DeWitt bracket analyzed in the multisymplectic context. Once our star-product is defined we are able to apply the Wigner-Weyl map in order to introduce a generalized version of Wick's theorem. Finally, we include a couple of examples to explicitly test our method: the real scalar field and the bosonic string. For both models we have encountered generalizations of the creation/annihilation relations, and also a generalization of the Virasoro algebra in the bosonic string case.

Mean-field methods, such as the Poisson-Boltzmann equation (PBE), are often used to calculate the electrostatic properties of molecular systems. In the past two decades, an enhancement of the PBE, the size-modified Poisson-Boltzmann equation (SMPBE), has been reported. Here, the PBE and the SMPBE are reevaluated for realistic molecular systems, namely, lipid bilayers, under eight different sets of input parameters. The SMPBE appears to reproduce the molecular dynamics simulation results better than the PBE only under specific parameter sets, but in general, it performs no better than the Stern layer correction of the PBE. These results emphasize the need for careful discussions of the accuracy of mean-field calculations on realistic systems with respect to the choice of parameters and call for reconsideration of the cost-efficiency and the significance of the current SMPBE formulation.

Interactions between surfaces and proteins occur in many vital processes and are crucial in biotechnology: the ability to control specific interactions is essential in fields like biomaterials, biomedical implants and biosensors. In the latter case, biosensor sensitivity hinges on ligand proteins adsorbing on bioactive surfaces with a favorable orientation, exposing reaction sites to target molecules. Protein adsorption, being a free-energy-driven process, is difficult to study experimentally. This paper develops and evaluates a computational model to study electrostatic interactions of proteins and charged nanosurfaces, via the Poisson-Boltzmann equation. We extended the implicit-solvent model used in the open-source code PyGBe to include surfaces of imposed charge or potential. This code solves the boundary integral formulation of the Poisson-Boltzmann equation, discretized with surface elements. PyGBe has at its core a treecode-accelerated Krylov iterative solver, resulting in O(N log N) scaling, with furt...

Concurrently coupled numerical simulations using heterogeneous solvers are powerful tools for modeling multiscale phenomena. However, major modifications to existing codes are often required to enable such simulations, posing significant difficulties in practice. In this paper we present a C++ library, i.e. the Multiscale Universal Interface (MUI), which is capable of facilitating the coupling effort for a wide range of multiscale simulations. The library adopts a header-only form with minimal external dependency and hence can be easily dropped into existing codes. A data sampler concept is introduced, combined with a hybrid dynamic/static typing mechanism, to create an easily customizable framework for solver-independent data interpretation. The library integrates MPI MPMD support and an asynchronous communication protocol to handle inter-solver information exchange irrespective of the solvers' own MPI awareness. Template metaprogramming is heavily employed to simultaneously improve runtime performance and c...

National Aeronautics and Space Administration — The uncertainty quantification methods developed under this program are designed for use with current state-of-the-art flow solvers developed by and in use at NASA....

Who provides better inputs to new product ideation tasks, problem solvers with expertise in the area for which new products are to be developed or problem solvers from “analogous” markets that are distant but share an analogous problem or need? Conventional wisdom appears to suggest that target...... that including problem solvers from analogous markets versus the target market accounts for almost two-thirds of the well-known effect of involving lead users instead of average problem solvers. This effect is further amplified when the analogous distance between the markets increases, i.e., when searching...... market expertise is indispensable, which is why most managers searching for new ideas tend to stay within their own market context even when they do search outside their firms' boundaries. However, in a unique symmetric experiment that isolates the effect of market origin, we find evidence...

This paper describes recent progress towards porting a Unified Flow Solver (UFS) to heterogeneous parallel computing. UFS is an adaptive kinetic-fluid simulation tool, which combines Adaptive Mesh Refinement (AMR) with automatic cell-by-cell selection of kinetic or fluid solvers based on continuum breakdown criteria. The main challenge of porting UFS to graphics processing units (GPUs) comes from the dynamically adapted mesh, which causes irregular data access. We describe the implementation of CUDA kernels for three modules in UFS: the direct Boltzmann solver using discrete velocity method (DVM), the Direct Simulation Monte Carlo (DSMC) module, and the Lattice Boltzmann Method (LBM) solver, all using octree Cartesian mesh with AMR. Double digit speedups on single GPU and good scaling for multi-GPU have been demonstrated.

In this paper we present a new family of approximate Riemann solvers for the numerical approximation of solutions of hyperbolic conservation laws. They are approximate, also referred to as incomplete, in the sense that the solvers avoid computing the characteristic decomposition of the flux Jacobian. Instead, they require only an estimate of the globally fastest wave speeds in both directions. Thus, this family of solvers is particularly efficient for large systems of conservation laws, i.e. with many different propagation speeds, and when no explicit expression for the eigensystem is available. Even though only fastest wave speeds are needed as input values, the new family of Riemann solvers reproduces all waves with less dissipation than HLL, which has the same prerequisites, requiring only one additional flux evaluation.

Full Text Available The hybrid solvers based on integral equation domain decomposition method (HS-DDM are developed for modeling of electromagnetic radiation. Based on the philosophy of “divide and conquer,” the IE-DDM divides the original multiscale problem into many closed nonoverlapping subdomains. For adjacent subdomains, the Robin transmission conditions ensure the continuity of currents, so the meshes of different subdomains can be allowed to be nonconformal. It also allows different fastsolvers to be used in different subdomains based on the property of different subdomains to reduce the time and memory consumption. Here, the multilevel fast multipole algorithm (MLFMA and hierarchical (H- matrices method are combined in the framework of IE-DDM to enhance the capability of IE-DDM and realize efficient solution of multiscale electromagnetic radiating problems. The MLFMA is used to capture propagating wave physics in large, smooth regions, while H-matrices are used to capture evanescent wave physics in small regions which are discretized with dense meshes. Numerical results demonstrate the validity of the HS-DDM.

In this paper,a one-dimensional bipolar Euler-Poisson system (a hydrodynamic model) from semiconductors or plasmas with boundary effects is considered.This system takes the form of Euler-Poisson with an electric field and frictional damping added to the momentum equations.The large-time behavior of uniformly bounded weak solutions to the initial-boundary value problem for the one-dimensional bipolar Euler-Poisson system is firstly presented.Next,two particle densities and the corresponding current momenta are verified to satisfy the porous medium equation and the classical Darcy's law time asymptotically.Finally,as a by-product,the quasineutral limit of the weak solutions to the initial-boundary value problem is investigated in the sense that the bounded L∞ entropy solution to the one-dimensional bipolar Euler-Poisson system converges to that of the corresponding one-dimensional compressible Euler equations with damping exponentially fast as t → +∞.As far as we know,this is the first result about the asymptotic behavior and the quasineutral limit for the one-dimensional bipolar Euler-Poisson system with boundary effects and a vacuum.

A Poisson process is one of the fundamental descriptions for relativistic particles: both fermions and bosons. A generalized linear photon wave equation in dispersive and homogeneous medium with dissipation is derived using the formulation of the Poisson process. This formulation provides a possible interpretation of the passage time of a photon moving in the medium, which never exceeds the speed of light in vacuum.

Starting from a Lagrangian formulation of the Vlasov-Coulomb system, canonical methods are used to define a Poisson structure for this system. Successive changes of representation then lead systematically to the noncanonical Lie-Poisson structure for functionals of the Vlasov distribution.

We consider Lagrangian-like submanifolds in certain even-dimensional 'symplectic-like' Poisson manifolds. We show, under suitable transversality hypotheses, that the pair consisting of the ambient Poisson manifold and the submanifold has unobstructed deformations and that the deformations automatically preserve the Lagrangian-like property.

In this note, the regularity of Poisson equation -△u = f with f lying in logarithmic function space Lp(LogL)a(Ω)(1＜p ＜∞, a ∈ R) is studied. The result of the note generalizes the W2,p estimate of Poisson equation in Lp(Ω).

Topology optimized architectures are designed and printed with programmable Poisson's ratios ranging from -0.8 to 0.8 over large deformations of 20% or more.......Topology optimized architectures are designed and printed with programmable Poisson's ratios ranging from -0.8 to 0.8 over large deformations of 20% or more....

We apply nonparametric Bayesian methods to study the problem of estimating the intensity function of an inhomogeneous Poisson process. To motivate our results we start by analyzing count data coming from a call center which we model as a Poisson process. This analysis is carried out using a certain

In this paper we generalize the aggregated premium income process from a constant rate process to a poisson process for the classical compound Poinsson risk model,then for the generalized model and the classical compound poisson risk model ,we respectively get its survival probability in finite time period in case of exponential claim amounts.

All Bianchi bialgebras have been obtained. By introducing a non-degenerate adjoint invariant inner product over these bialgebras the associated Drinfeld doubles have been constructed, then by calculating the coupling matrices for these bialgebras several \\sigma-models with Poisson-Lie symmetry have been obtained. Two simple examples as prototypes of Poisson-Lie dual models have been given.

Python is a programming language that has gained a lot of popularity during the last 15 years, and as a very easy-to-learn and flexible scripting language it is very well suited for computa- tional science, both in mathematics and in physics. Diffpack is a PDE library written in C++, made for easier implementation of both smaller PDE solvers and for larger libraries of simu- lators. It contains large class hierarchies for different solvers, grids, arrays, parallel computing and almost everyth...

AN INTERACTIVE CHEMICAL EQUILIBRIUM SOLVER FOR THE PERSONAL COMPUTER Charles Hugh Negus Felix J. Pierce, Chairman Mechanical Engineering The Virginia Tech Equilibrium Chemistry (VTEC) code is a keyboard interactive, user friendly, chemical equilibrium solver for use on a personal computer. The code is particularly suitable for a teaching / learning environment. For a set of reactants at a defined thermodynamic state given by a user, the program will select all species...

Poisson's ratio in materials is governed by the following aspects of the microstructure: the presence of rotational degrees of freedom, non-affine deformation kinematics, or anisotropic structure. Several structural models are examined. The non-affine kinematics are seen to be essential for the production of negative Poisson's ratios for isotropic materials containing central force linkages of positive stiffness. Non-central forces combined with pre-load can also give rise to a negative Poisson's ratio in isotropic materials. A chiral microstructure with non-central force interaction or non-affine deformation can also exhibit a negative Poisson's ratio. Toughness and damage resistance in these materials may be affected by the Poisson's ratio itself, as well as by generalized continuum aspects associated with the microstructure.

We are developing a general capability to adaptively solve phase space evolution equations mixing particle and continuum techniques in an adaptive manner. The multi-scale approach is achieved using wavelet decompositions which allow phase space density estimation to occur with scale dependent increased accuracy and variable time stepping. Possible improvements on the SFK method of Larson are discussed, including the use of multiresolution analysis based Richardson-Lucy Iteration, adaptive step size control in explicit vs implicit approaches. Examples will be shown with KEEN waves and KEEPN (Kinetic Electrostatic Electron Positron Nonlinear) waves, which are the pair plasma generalization of the former, and have a much richer span of dynamical behavior. WAKES techniques are well suited for the study of driven and released nonlinear, non-stationary, self-organized structures in phase space which have no fluid, limit nor a linear limit, and yet remain undamped and coherent well past the drive period. The work reported here is based on the Vlasov-Poisson model of plasma dynamics. Work supported by a Grant from the AFOSR.

A new implicit algorithm has been developed for the solution of the time-dependent, viscous and resistive single fluid magnetohydrodynamic (MHD) equations. The algorithm is based on an approximate Riemann solver for the hyperbolic fluxes and central differencing applied on a staggered grid for the parabolic fluxes. The algorithm employs a locally aligned coordinate system that allows the solution to the Riemann problems to be solved in a natural direction, normal to cell interfaces. The result is an original scheme that is robust and reduces the complexity of the flux formulas. The evaluation of the parabolic fluxes is also implemented using a locally aligned coordinate system, this time on the staggered grid. The implicit formulation employed by WARP3 is a two level scheme that was applied for the first time to the single fluid MHD model. The flux Jacobians that appear in the implicit scheme are evaluated numerically. The linear system that results from the implicit discretization is solved using a robust symmetric Gauss-Seidel method. The code has an explicit mode capability so that implementation and test of new algorithms or new physics can be performed in this simpler mode. Last but not least the code was designed and written to run on parallel computers so that complex, high resolution runs can be per formed in hours rather than days. The code has been benchmarked against analytical and experimental gas dynamics and MHD results. The benchmarks consisted of one-dimensional Riemann problems and diffusion dominated problems, two-dimensional supersonic flow over a wedge, axisymmetric magnetoplasmadynamic (MPD) thruster simulation and three-dimensional supersonic flow over intersecting wedges and spheromak stability simulation. The code has been proven to be robust and the results of the simulations showed excellent agreement with analytical and experimental results. Parallel performance studies showed that the code performs as expected when run on parallel

The complexity of constraints is a major obstacle for constraint-based software verification. Automatic constraint solvers are fundamentally incomplete: input constraints often build on some undecidable theory or some theory the solver does not support. This paper proposes and evaluates several randomized solvers to address this issue. We compare the effectiveness of a symbolic solver (CVC3), a random solver, three hybrid solvers (i.e., mix of random and symbolic), and two heuristic search solvers. We evaluate the solvers on two benchmarks: one consisting of manually generated constraints and another generated with a concolic execution of 8 subjects. In addition to fully decidable constraints, the benchmarks include constraints with non-linear integer arithmetic, integer modulo and division, bitwise arithmetic, and floating-point arithmetic. As expected symbolic solving (in particular, CVC3) subsumes the other solvers for the concolic execution of subjects that only generate decidable constraints. For the remaining subjects the solvers are complementary.

The formulation and time discretization of problems in meteorology are often tailored to the type of efficient solvers available for use on the discrete problems obtained. A common procedure is to formulate the problem so that a constant (or latitude-dependent) coefficient Poisson-like equation results at each time step, which is then solved using spectral methods. This both limits the scope of problems that can be handled and requires linearization by forward extrapolation of nonlinear terms, which, in turn, requires filtering to control noise. Multigrid methods do not suffer these limitations, and can be applied directly to systems of nonlinear equations with variable coefficients. Here, a global barotropic semi-Lagrangian model, developed by the authors, is presented which results in a system of three coupled nonlinear equations to be solved at each time step. A multigrid method for the solution of these equations is described, and results are presented.

We consider a queue where the server is the Euclidean space, and the customers are random closed sets (RACS) of the Euclidean space. These RACS arrive according to a Poisson rain and each of them has a random service time (in the case of hail falling on the Euclidean plane, this is the height of the hailstone, whereas the RACS is its footprint). The Euclidean space serves customers at speed 1. The service discipline is a hard exclusion rule: no two intersecting RACS can be served simultaneously and service is in the First In First Out order: only the hailstones in contact with the ground melt at speed 1, whereas the other ones are queued; a tagged RACS waits until all RACS arrived before it and intersecting it have fully melted before starting its own melting. We give the evolution equations for this queue. We prove that it is stable for a sufficiently small arrival intensity, provided the typical diameter of the RACS and the typical service time have finite exponential moments. We also discuss the percolatio...

Starting with the well-defined product of quantum fields at two spacetime points, we explore an associated Poisson structure for classical field theories within the deformation quantization formalism. We realize that the induced star-product is naturally related to the standard Moyal product through an appropriate causal Green’s functions connecting points in the space of classical solutions to the equations of motion. Our results resemble the Peierls-DeWitt bracket that has been analyzed in the multisymplectic context. Once our star-product is defined, we are able to apply the Wigner-Weyl map in order to introduce a generalized version of Wick’s theorem. Finally, we include some examples to explicitly test our method: the real scalar field, the bosonic string and a physically motivated nonlinear particle model. For the field theoretic models, we have encountered causal generalizations of the creation/annihilation relations, and also a causal generalization of the Virasoro algebra for the bosonic string. For the nonlinear particle case, we use the approximate solution in terms of the Green’s function, in order to construct a well-behaved causal bracket.

We revisit in one dimension the waterbag method to solve numerically Vlasov-Poisson equations. In this approach, the phase-space distribution function $f(x,v)$ is initially sampled by an ensemble of patches, the waterbags, where $f$ is assumed to be constant. As a consequence of Liouville theorem it is only needed to follow the evolution of the border of these waterbags, which can be done by employing an orientated, self-adaptive polygon tracing isocontours of $f$. This method, which is entropy conserving in essence, is very accurate and can trace very well non linear instabilities as illustrated by specific examples. As an application of the method, we generate an ensemble of single waterbag simulations with decreasing thickness, to perform a convergence study to the cold case. Our measurements show that the system relaxes to a steady state where the gravitational potential profile is a power-law of slowly varying index $\\beta$, with $\\beta$ close to $3/2$ as found in the literature. However, detailed analys...

We revisit the integer lattice (IL) method to numerically solve the Vlasov-Poisson equations, and show that a slight variant of the method is a very easy, viable, and efficient numerical approach to study the dynamics of self-gravitating, collisionless systems. The distribution function lives in a discretized lattice phase-space, and each time-step in the simulation corresponds to a simple permutation of the lattice sites. Hence, the method is Lagrangian, conservative, and fully time-reversible. IL complements other existing methods, such as N-body/particle mesh (computationally efficient, but affected by Monte Carlo sampling noise and two-body relaxation) and finite volume (FV) direct integration schemes (expensive, accurate but diffusive). We also present improvements to the FV scheme, using a moving-mesh approach inspired by IL, to reduce numerical diffusion and the time-step criterion. Being a direct integration scheme like FV, IL is memory limited (memory requirement for a full 3D problem scales as N6, where N is the resolution per linear phase-space dimension). However, we describe a new technique for achieving N4 scaling. The method offers promise for investigating the full 6D phase-space of collisionless systems of stars and dark matter.

We revisit the integer lattice (IL) method to numerically solve the Vlasov-Poisson equations, and show that a slight variant of the method is a very easy, viable, and efficient numerical approach to study the dynamics of self-gravitating, collisionless systems. The distribution function lives in a discretized lattice phase-space, and each time-step in the simulation corresponds to a simple permutation of the lattice sites. Hence, the method is Lagrangian, conservative, and fully time-reversible. IL complements other existing methods, such as N-body/particle mesh (computationally efficient, but affected by Monte-Carlo sampling noise and two-body relaxation) and finite volume (FV) direct integration schemes (expensive, accurate but diffusive). We also present improvements to the FV scheme, using a moving mesh approach inspired by IL, to reduce numerical diffusion and the time-step criterion. Being a direct integration scheme like FV, IL is memory limited (memory requirement for a full 3D problem scales as N^6, ...

The time dependent chemical rate equations arising from astrochemical kinetics problems are described by a system of stiff ordinary differential equations (ODEs). In this paper, using three astrochemical models of varying physical and computational complexity, and hence different degrees of stiffness, we present a comprehensive performance survey of a set of well-established ODE solver packages from the ODEPACK collection, namely LSODE, LSODES, VODE and VODPK. For completeness, we include results from the GEAR package in one of the test models. The results demonstrate that significant performance improvements can be obtained over GEAR which is still being used by many astrochemists by default. We show that a simple appropriate ordering of the species set results in a substantial improvement in the performance of the tested ODE solvers. The sparsity of the associated Jacobian matrix can be exploited and results using the sparse direct solver routine LSODES show an extensive reduction in CPU time without any loss in accuracy. We compare the performance and the computed abundances of one model with a 175 species set and a reduced set of 88 species, keeping all physical and chemical parameters identical with both sets.We found that the calculated abundances using two different size models agree quite well. However, with no extra computational effort and more reliable results, it is possible for the computation to be many times faster with the larger species set than the reduced set, depending on the use of solvers, the ordering and the chosen options. It is also shown that though a particular solver with certain chosen parameters may have severe difficulty or even fail to complete a run over the required integration time, another solver can easily complete the run with a wider range of control parameters and options. As a result of the superior performance of LSODES for the solution of astrochemical kinetics systems, we have tailor-made a sparse version of the VODE

Nowadays, most researchers have access to computer clusters. For the community developing numerical applications in geodynamics, this constitutes a very important potential: besides that current applications can be speeded up, much bigger problems can be solved. This is particularly relevant in 3D applications. However, current practical experiments in geodynamic high-performance applications normally end with the successful demonstration of the potential by exploring the performance of the simplest example (typically the Poissonsolver); more advanced practical examples are rare. For this reason, we optimize algorithms for 3D scalar problems and 3D mechanics and design concise, educational Fortran 90 templates that allow other researchers to easily plug in their own geodynamic computations: in these templates, the geodynamic computations are entirely separated from the technical programming needed for the parallelized running on a computer cluster; additionally, we develop our code with minimal syntactical differences from the MATLAB language, such that prototypes of the desired geodynamic computations can be programmed in MATLAB and then copied into the template with only minimal syntactical changes. High-performance programming requires to a big extent taking into account the specificities of the available hardware. The hardware of the world's largest CPU clusters is very different from the one of a modern mid-sized CPU cluster. In this context, we investigate the performance of basic memory-bounded geodynamic solvers on the large-sized BlueGene/P cluster, having 13 Gb/s peak memory bandwidth, and compare it with the performance of a typical modern mid-sized CPU cluster, having 100 Gb/s peak memory bandwidth. A memory-bounded solver's performance depends only on the amount of data required for its computations and on the speed this data can be read from memory (or from the CPUs' cache). In consequence, we speed up the solvers by optimizing memory access and CPU

The standard Poisson structure on the rectangular matrix variety Mm,n(C) is\\ud investigated, via the orbits of symplectic leaves under the action of the maximal torus T ⊂\\ud GLm+n(C). These orbits, finite in number, are shown to be smooth irreducible locally closed\\ud subvarieties of Mm,n(C), isomorphic to intersections of dual Schubert cells in the full flag\\ud variety of GLm+n(C). Three different presentations of the T-orbits of symplectic leaves in\\ud Mm,n(C) are obtained – (a) as pu...

The continuum theory applied to bimolecular electrostatics leads to an implicit-solvent model governed by the Poisson-Boltzmann equation. Solvers relying on a boundary integral representation typically do not consider features like solvent-filled cavities or ion-exclusion (Stern) layers, due to the added difficulty of treating multiple boundary surfaces. This has hindered meaningful comparisons with volume-based methods, and the effects on accuracy of including these features has remained unknown. This work presents a solver called PyGBe that uses a boundary-element formulation and can handle multiple interacting surfaces. It was used to study the effects of solvent-filled cavities and Stern layers on the accuracy of calculating solvation energy and binding energy of proteins, using the well-known APBS finite-difference code for comparison. The results suggest that if required accuracy for an application allows errors larger than about 2%, then the simpler, single-surface model can be used. When calculating b...

We address the problem of classifying discrete differential-geometric Poisson brackets (dDGPBs) of any fixed order on target space of dimension 1. It is proved that these Poisson brackets (PBs) are in one-to-one correspondence with the intersection points of certain projective hypersurfaces. In addition, they can be reduced to cubic PB of standard Volterra lattice by discrete Miura-type transformations. Finally, improving a consolidation lattice procedure, we obtain new families of non-degenerate, vector-valued and first order dDGPBs, which can be considered in the framework of admissible Lie-Poisson group theory.

We consider a class of observation-driven Poisson count processes where the current value of the accompanying intensity process depends on previous values of both processes. We show under a contractive condition that the bivariate process has a unique stationary distribution and that a stationary version of the count process is absolutely regular. Moreover, since the intensities can be written as measurable functionals of the count variables, we conclude that the bivariate process is ergodic. As an important application of these results, we show how a test method previously used in the case of independent Poisson data can be used in the case of Poisson count processes.

A method to obtain the probability distribution of the interarrival times of jump occurrences in systems driven by state-dependent Poisson noise is proposed. Such a method uses the survivor function obtained by a modified version of the master equation associated to the stochastic process under analysis. A model for the timing of human activities shows the capability of state-dependent Poisson noise to generate power-law distributions. The application of the method to a model for neuron dynamics and to a hydrological model accounting for land-atmosphere interaction elucidates the origin of characteristic recurrence intervals and possible persistence in state-dependent Poisson models.

A method to obtain the probability distribution of the interarrival times of jump occurrences in systems driven by state-dependent Poisson noise is proposed. Such a method uses the survivor function obtained by a modified version of the master equation associated to the stochastic process under analysis. A model for the timing of human activities shows the capability of state-dependent Poisson noise to generate power-law distributions. The application of the method to a model for neuron dynamics and to a hydrological model accounting for land-atmosphere interaction elucidates the origin of characteristic recurrence intervals and possible persistence in state-dependent Poisson models.

Nonstationary Poisson processes are appropriate in many applications, including disease studies, transportation, finance, and social policy. The authors review the risks of ignoring nonstationarity in Poisson processes and demonstrate three algorithms for generation of Poisson processes with piec......Nonstationary Poisson processes are appropriate in many applications, including disease studies, transportation, finance, and social policy. The authors review the risks of ignoring nonstationarity in Poisson processes and demonstrate three algorithms for generation of Poisson processes...

It is well known that for the Eulerian equations the numerical schemes that can accurately capture contact discontinuity usually suffer from some disastrous carbuncle phenomenon, while some more dissipative schemes, such as the HLL scheme, are free from this kind of shock instability. Hybrid schemes to combine a dissipative flux with a less dissipative flux can cure the shock instability, but also may lead to other problems, such as certain arbitrariness of choosing switching parameters or contact interface becoming smeared. In order to overcome these drawbacks, this paper proposes a simple and robust HLLC-type Riemann solver for inviscid, compressible gas flows, which is capable of preserving sharp contact surface and is free from instability. The main work is to construct a HLL-type Riemann solver and a HLLC-type Riemann solver by modifying the shear viscosity of the original HLL and HLLC methods. Both of the two new schemes are positively conservative under some typical wavespeed estimations. Moreover, a linear matrix stability analysis for the proposed schemes is accomplished, which illustrates the HLLC-type solver with shear viscosity is stable whereas the HLL-type solver with vorticity wave is unstable. Our arguments and numerical experiments demonstrate that the inadequate dissipation associated to the shear wave may be a unique reason to cause the instability.

A relation between a gravity on Poisson manifolds proposed in arXiv:1508.05706 and the Einstein gravity is investigated. The compatibility of the Poisson and Riemann structures defines a unique connection, the contravariant Levi-Civita connection, and leads to the idea of the contravariant gravity. The Einstein-Hilbert-type action includes couplings between the metric and the Poisson tensor. The Weyl transformation is studied to reveal properties of those interactions. It is argued that the theory can have an equivalent description in terms of the Einstein gravity coupled to matter. As an example, it is shown that the contravariant gravity on a two-dimensional Poisson manifold has another description by a real scalar field coupling to the metric in a specific manner.

This study gives attention to indicators in predictive power of the Generalized Linear Model (GLM) which are widely used; however, often having some restrictions. We are interested in regression correlation coefficient for a Poisson regression model. This is a measure of predictive power, and defined by the relationship between the dependent variable (Y) and the expected value of the dependent variable given the independent variables [E(Y|X)] for the Poisson regression model. The dependent variable is distributed as Poisson. The purpose of this research was modifying regression correlation coefficient for Poisson regression model. We also compare the proposed modified regression correlation coefficient with the traditional regression correlation coefficient in the case of two or more independent variables, and having multicollinearity in independent variables. The result shows that the proposed regression correlation coefficient is better than the traditional regression correlation coefficient based on Bias and the Root Mean Square Error (RMSE).

This paper investigates neuron activation statistics in artificial neural networks employing stochastic arithmetic. It is shown that a doubly stochastic Poisson process is an appropriate model for the signals in these circuits.

Previous models of laser Doppler velocimeter (LDV) systems have not adequately described dual-scatter signals in a manner useful for analysis and simulation of low-level photon-limited signals. At low photon rates, an LDV signal at the output of a photomultiplier tube is a compound nonhomogeneous filtered Poisson process, whose intensity function is another (slower) Poisson process with the nonstationary rate and frequency parameters controlled by a random flow (slowest) process. In the present paper, generalized Poisson shot noise models are developed for low-level LDV signals. Theoretical results useful in detection error analysis and simulation are presented, along with measurements of burst amplitude statistics. Computer generated simulations illustrate the difference between Gaussian and Poisson models of low-level signals.

We derive an exact probabilistic representation for the evolution of a Hubbard model with site- and spin-dependent hopping coefficients and site-dependent interactions in terms of an associated stochastic dynamics of a collection of Poisson processes.

We derive an exact probabilistic representation for the evolution of a Hubbard model with site- and spin-dependent hopping coefficients and site-dependent interactions in terms of an associated stochastic dynamics of a collection of Poisson processes.

The idea of this work is to compare a new positive and entropy stable approximate Riemann solver by Francois Bouchut with a state-of the-art algorithm for astrophysical fluid dynamics. We implemented the new Riemann solver into an astrophysical PPM-code, the Prometheus code, and also made a version with a different, more theoretically grounded higher order algorithm than PPM. We present shock tube tests, two-dimensional instability tests and forced turbulence simulations in three dimensions. We find subtle differences between the codes in the shock tube tests, and in the statistics of the turbulence simulations. The new Riemann solver increases the computational speed without significant loss of accuracy.

In this research we are particularly interested in extending the robustness of multigrid solvers to encounter complex systems related to subsurface reservoir applications for flow problems in porous media. In many cases, the step for solving the pressure filed in subsurface flow simulation becomes a bottleneck for the performance of the simulator. For solving large sparse linear system arising from MPFA discretization, we choose multigrid methods as the linear solver. The possible difficulties and issues will be addressed and the corresponding remedies will be studied. As the multigrid methods are used as the linear solver, the simulator can be parallelized (although not trivial) and the high-resolution simulation become feasible, the ultimately goal which we desire to achieve.

Graphics processing units have gained popularities in scientific computing over past several years due to their outstanding parallel computing capability. Computational fluid dynamics applications involve large amounts of calculations, therefore a latest GPU card is preferable of which the peak computing performance and memory bandwidth are much better than a contemporary high-end CPU. We herein focus on the detailed implementation of our GPU targeting Reynolds-averaged Navier-Stokes equations solver based on finite-volume method. The solver employs a vertex-centered scheme on unstructured grids for the sake of being capable of handling complex topologies. Multiple optimizations are carried out to improve the memory accessing performance and kernel utilization. Both steady and unsteady flow simulation cases are carried out using explicit Runge-Kutta scheme. The solver with GPU acceleration in this paper is demonstrated to have competitive advantages over the CPU targeting one.

This paper presents an evaluation of the design decisions made in four state-of-the-art constraint solvers; Choco, ECLiPSe, Gecode, and Minion. To assess the impact of design decisions, instances of the five problem classes n-Queens, Golomb Ruler, Magic Square, Social Golfers, and Balanced Incomplete Block Design are modelled and solved with each solver. The results of the experiments are not meant to give an indication of the performance of a solver, but rather investigate what influence the choice of algorithms and data structures has. The analysis of the impact of the design decisions focuses on the different ways of memory management, behaviour with increasing problem size, and specialised algorithms for specific types of variables. It also briefly considers other, less significant decisions.

We present a mathematical model for communication subject to both network interference and noise. We introduce a framework where the interferers are scattered according to a spatial Poisson process, and are operating asynchronously in a wireless environment subject to path loss, shadowing, and multipath fading. We consider both cases of slow and fast-varying interferer positions. The paper is comprised of two separate parts. In Part I, we determine the distribution of the aggregate network interference at the output of a linear receiver. We characterize the error performance of the link, in terms of average and outage probabilities. The proposed model is valid for any linear modulation scheme (e.g., M-ary phase shift keying or M-ary quadrature amplitude modulation), and captures all the essential physical parameters that affect network interference. Our work generalizes the conventional analysis of communication in the presence of additive white Gaussian noise and fast fading, allowing the traditional results...

In this note, we gauge the rigid vectorial supersymmetry of the two-dimensional Poisson sigma model presented in arXiv:1503.05625. We show that the consistency of the construction does not impose any further constraints on the differential Poisson algebra geometry than those required for the ungauged model. We conclude by proposing that the gauged model provides a first-quantized framework for higher spin gravity.

The algebraic structure and the Poisson method for a weakly nonholonomic system are studied.The differential equations of motion of the system can be written in a contravariant algebra form and its algebraic structure is discussed.The Poisson theory for the systems which possess Lie algebra structure is generalized to the weakly nonholonomic system.An example is given to illustrate the application of the result.

In this note, we gauge the rigid vectorial supersymmetry of the two-dimensional Poisson sigma model presented in arXiv:1503.05625. We show that the consistency of the construction does not impose any further constraints on the differential Poisson algebra geometry than those required for the ungauged model. We conclude by proposing that the gauged model provides a first-quantized framework for higher spin gravity.

Let $B_s$ be a three dimensional Brownian motion and $\\omega(dx)$ be an independent Poisson field on $\\mathbb{R}^3$. It is proved that for any $t>0$, conditionally on $\\omega(\\cdot)$, \\label{*} \\mathbb{E}_0 \\exp\\{\\theta \\int_0^t \\bar{V}(B_s) ds\\} \\ 1/16, where $\\bar{V}(x)$ is the renormalized Poisson potential

In this note, we gauge the rigid vectorial supersymmetry of the two-dimensional Poisson sigma model presented in arXiv:1503.05625. We show that the consistency of the construction does not impose any further constraints on the differential Poisson algebra geometry than those required for the ungauged model. We conclude by proposing that the gauged model provides a first-quantized framework for higher spin gravity.

In this note, we gauge the rigid vectorial supersymmetry of the two-dimensional Poisson sigma model presented in arXiv:1503.05625. We show that the consistency of the construction does not impose any further constraints on the differential Poisson algebra geometry than those required for the ungauged model. We conclude by proposing that the gauged model provides a first-quantized framework for higher spin gravity.

Full Text Available Given a Poisson process on a bounded interval, its random geometric graph is the graph whose vertices are the points of the Poisson process, and edges exist between two points if and only if their distance is less than a fixed given threshold. We compute explicitly the distribution of the number of connected components of this graph. The proof relies on inverting some Laplace transforms.

We review a particular class of approximate Riemann solvers in the context of the equations of ideal relativistic magnetohydrodynamics. Commonly prefixed as Harten-Lax-van Leer (HLL), this family of solvers approaches the solution of the Riemann problem by providing suitable guesses to the outermots characteristic speeds, without any prior knowledge of the solution. By requiring consistency with the integral form of the conservation law, a simplified set of jump conditions with a reduced number of characteristic waves may be obtained. The degree of approximation crucially depends on the wave pattern used in prepresnting the Riemann fan arising from the initial discontinuity breakup. In the original HLL scheme, the solution is approximated by collapsing the full characteristic structure into a single average state enclosed by two outermost fast mangnetosonic speeds. On the other hand, HLLC and HLLD improves the accuracy of the solution by restoring the tangential and Alfvén modes therefore leading to a representation of the Riemann fan in terms of 3 and 5 waves, respectively.

In this paper we modify a fast heuristic solver for the Linear Sum Assignment Problem (LSAP) for use on Graphical Processing Units (GPUs). The motivating scenario is an industrial application for P2P live streaming that is moderated by a central node which is periodically solving LSAP instances for assigning peers to one another. The central node needs to handle LSAP instances involving thousands of peers in as near to real-time as possible. Our findings are generic enough to be applied in other contexts. Our main result is a parallel version of a heuristic algorithm called Deep Greedy Switching (DGS) on GPUs using the CUDA programming language. DGS sacrifices absolute optimality in favor of low computation time and was designed as an alternative to classical LSAP solvers such as the Hungarian and auctioning methods. The contribution of the paper is threefold: First, we present the process of trial and error we went through, in the hope that our experience will be beneficial to adopters of GPU programming for...

We describe a parallel iterative least squares solver named \\texttt{LSRN} that is based on random normal projection. The solver computes the unique min-length solution to $\\min_{x \\in \\mathbb{R}^n} \\|A x - b\\|_2$, where $A \\in \\mathbb{R}^{m \\times n}$ can be either full rank or rank-deficient, and where $m \\gg n$ or $m \\ll n$. Since $A$ is only involved in matrix-matrix and matrix-vector multiplications, $A$ can be a dense matrix, a sparse matrix, or a linear operator; and, in addition, \\texttt{LSRN} automatically speeds up on sparse matrices and with fast linear operators. The preconditioning phase consists of a random normal projection, which is embarrassingly parallel, and a singular value decomposition of size $\\lceil \\gamma \\min(m,n) \\rceil \\times \\min(m,n)$, where $\\gamma$ is moderately larger than 1, e.g., $\\gamma = 2$. We prove that the preconditioned system is well-conditioned, with a strong concentration result on the extreme singular values, and hence that the number of iterations is fully predicta...

In the nested approach to structural optimization, most of the computational effort is invested in the solution of the analysis equations. In this study, it is suggested to reduce this computational cost by using an approximation to the solution of the analysis problem, generated by a Krylov...... subspace iterative solver. By choosing convergence criteria for the iterative solver that are strongly related to the optimization objective and to the design sensitivities, it is possible to terminate the iterative solution of the nested equations earlier compared to traditional convergence measures...

This article proposes to add a simple term to an iterative algebraic equation solver with an order n convergence rate, and to raise the order of convergence to (2n - 1). In particular, a simple algebraic equation solver with the 5th order convergence but uses only 4 function values in each iteration, is described in details. When this scheme is applied to a Newton-Raphson method of the quadratic convergence for a system of algebraic equations, a cubic convergence can be achieved with an low overhead cost of function evaluation that can be ignored as the size of the system increases.

As part of the National Cycle Program (NCP), a powerful new numerical solver has been developed to support the simulation of aeropropulsion systems. This software uses a hierarchical object-oriented design. It can provide steady-state and time-dependent solutions to nonlinear and even discontinuous problems typically encountered when aircraft and spacecraft propulsion systems are simulated. It also can handle constrained solutions, in which one or more factors may limit the behavior of the engine system. Timedependent simulation capabilities include adaptive time-stepping and synchronization with digital control elements. The NCP solver is playing an important role in making the NCP a flexible, powerful, and reliable simulation package.

As high-resolution observational data become more common, the demand for numerical simulations of crustal deformation using 3-D high-fidelity modelling is increasing. To increase the efficiency of performing numerical simulations with high computation costs, we developed a fastsolver using heterogeneous computing, with graphics processing units (GPUs) and central processing units, and then used the solver in crustal deformation computations. The solver was based on an iterative solver and was devised so that a large proportion of the computation was calculated more quickly using GPUs. To confirm the utility of the proposed solver, we demonstrated a numerical simulation of the coseismic slip distribution estimation, which requires 360 000 crustal deformation computations with 82 196 106 degrees of freedom.

) for the Poisson distribution is also well known, but has not become generally used. This is primarily because, in contrast to non-linear least squares fitting, there has been no quick, robust, and general fitting method. In the field of fluorescence lifetime spectroscopy and imaging, there have been some efforts to use this estimator through minimization routines such as Nelder-Mead optimization, exhaustive line searches, and Gauss-Newton minimization. Minimization based on specific one- or multi-exponential models has been used to obtain quick results, but this procedure does not allow the incorporation of the instrument response, and is not generally applicable to models found in other fields. Methods for using the MLE for Poisson-distributed data have been published by the wider spectroscopic community, including iterative minimization schemes based on Gauss-Newton minimization. The slow acceptance of these procedures for fitting event counting histograms may also be explained by the use of the ubiquitous, fast Levenberg-Marquardt (L-M) fitting procedure for fitting non-linear models using least squares fitting (simple searches obtain {approx}10000 references - this doesn't include those who use it, but don't know they are using it). The benefits of L-M include a seamless transition between Gauss-Newton minimization and downward gradient minimization through the use of a regularization parameter. This transition is desirable because Gauss-Newton methods converge quickly, but only within a limited domain of convergence; on the other hand the downward gradient methods have a much wider domain of convergence, but converge extremely slowly nearer the minimum. L-M has the advantages of both procedures: relative insensitivity to initial parameters and rapid convergence. Scientists, when wanting an answer quickly, will fit data using L-M, get an answer, and move on. Only those that are aware of the bias issues will bother to fit using the more appropriate MLE

Full Text Available The magnetic field effect on laminar natural convection flow is investigated in a filled enclosure with internal heat generation using two-dimensional numerical simulation. The enclosure is heated by a uniform volumetric heat density and walls have constant temperature. A fixed magnetic field is applied to the enclosure. The dimensionless governing equations are solved numerically for the stream function, vorticity and temperature using finite difference method for various Rayleigh (Ra and Hartmann (Ha numbers in MATLAB software. The stream function equation is solved using fastPoisson's equation solver on a rectangular grid (POICALC function in MATLAB, voricity and temperature equations are solved using red-black Gauss-Seidel and bi-conjugate gradient stabilized (BiCGSTAB methods respectively. The results show that the strength of the magnetic field has significant effects on the flow and temperature fields. For the square cavity, the maximum temperature reduces with increasing Ra number. It is also observed that at low Ra number, location of the maximum temperature is at the centre of the cavity and it shifts upwards with increase in Ra number. Circulation inside the enclosure and therefore the convection becomes stronger as the Ra number increases while the magnetic field suppresses the convective flow and the heat transfer rate. The ratio of the Lorentz force to the buoyancy force (Ha2/Ra is as an index to compare the contribution of natural convection and magnetic field strength on heat transfer.

Marching on in time (MOT)-based integral equation solvers represent an increasingly appealing avenue for analyzing transient electromagnetic interactions with large and complex structures. MOT integral equation solvers for analyzing electromagnetic scattering from perfect electrically conducting objects are obtained by enforcing electric field boundary conditions and implicitly time advance electric surface current densities by iteratively solving sparse systems of equations at all time steps. Contrary to finite difference and element competitors, these solvers apply to nonlinear and multi-scale structures comprising geometrically intricate and deep sub-wavelength features residing atop electrically large platforms. Moreover, they are high-order accurate, stable in the low- and high-frequency limits, and applicable to conducting and penetrable structures represented by highly irregular meshes. This presentation reviews some recent advances in the parallel implementations of time domain integral equation solvers, specifically those that leverage multilevel plane-wave time-domain algorithm (PWTD) on modern manycore computer architectures including graphics processing units (GPUs) and distributed memory supercomputers. The GPU-based implementation achieves at least one order of magnitude speedups compared to serial implementations while the distributed parallel implementation are highly scalable to thousands of compute-nodes. A distributed parallel PWTD kernel has been adopted to solve time domain surface/volume integral equations (TDSIE/TDVIE) for analyzing transient scattering from large and complex-shaped perfectly electrically conducting (PEC)/dielectric objects involving ten million/tens of millions of spatial unknowns.

Full Text Available In a recent paper cite{zara} a parallel direct solver for the linear systems arising from elliptic partial differential equations has been proposed. The aim of this note is to present the initial evaluation of the performance characteristics of this algorithm on Beowulf-type cluster. In this context the performance of PVM and MPI based implementations is compared.

Solving problems is not only a goal of mathematical learning. Students acquire ways of thinking, habits of persistence and curiosity, and confidence in unfamiliar situations by learning to solve problems. In fact, there were students who had difficulty in solving problems. The students were naive problem solvers. This research aimed to describe…

We consider a conservation law on a network and generic Riemann solvers at nodes depending on parameters, which can be seen as control functions. Assuming that the parameters have bounded variation as functions of time, we prove existence of solutions to Cauchy problems on the whole network.

We develop a performance prediction model for a parallelized sparse lattice Boltzmann solver and present performance results for simulations of flow in a variety of complex geometries. A special focus is on partitioning and memory/load balancing strategy for geometries with a high solid fraction and

In a recent paper cite{zara} a parallel direct solver for the linear systems arising from elliptic partial differential equations has been proposed. The aim of this note is to present the initial evaluation of the performance characteristics of this algorithm on Beowulf-type cluster. In this context the performance of PVM and MPI based implementations is compared.

This paper describes the application of an adaptive-grid finite-difference solver to some time-dependent three-dimensional systems of partial differential equations. The code is a 3D extension of the 2D code VLUGR2[3].

We present an exact algorithm for identification of deterministic finite automata (DFA) which is based on satisfiability (SAT) solvers. Despite the size of the low level SAT representation, our approach seems to be competitive with alternative techniques. Our contributions are threefold: First, we p

Hypersonic hybrid hydrodynamic-molecular gas flow solvers are required to satisfy the two essential requirements of any high-speed reacting code, these being physical accuracy and computational efficiency. The James Weir Fluids Laboratory at the University of Strathclyde is currently developing an open-source hybrid code which will eventually reconcile the direct simulation Monte-Carlo method, making use of the OpenFOAM application called dsmcFoam, and the newly coded open-source two-temperature computational fluid dynamics solver named hy2Foam. In conjunction with employing the CVDV chemistry-vibration model in hy2Foam, novel use is made of the QK rates in a CFD solver. In this paper, further testing is performed, in particular with the CFD solver, to ensure its efficacy before considering more advanced test cases. The hy2Foam and dsmcFoam codes have shown to compare reasonably well, thus providing a useful basis for other codes to compare against.

In this paper, a scalable parallel solver is proposed for H(div) problems discretized by arbitrary order finite elements on general unstructured meshes. The solver is based on hybridization and algebraic multigrid (AMG). Unlike some previously studied H(div) solvers, the hybridization solver does not require discrete curl and gradient operators as additional input from the user. Instead, only some element information is needed in the construction of the solver. The hybridization results in a H1-equivalent symmetric positive definite system, which is then rescaled and solved by AMG solvers designed for H1 problems. Weak and strong scaling of the method are examined through several numerical tests. Our numerical results show that the proposed solver provides a promising alternative to ADS, a state-of-the-art solver [12], for H(div) problems. In fact, it outperforms ADS for higher order elements.

@@ The completely integrable Hamiltonian systems have been applied to physics and mechanics intensively. We generate a family of completely integrable Hamiltonian systems from some kinds of exact Poisson structures in R3 by the realization of the Poisson algebra. Moreover, we prove that there is a Poisson algebra which cannot be realized by an exact Poisson structure.

We observe [Launois and Lecoutre, Trans. Am. Math. Soc. 368:755-785, 2016, Proposition 4.1] that Poisson polynomial extensions appear as semiclassical limits of a class of Ore extensions. As an application, a Poisson generalized Weyl algebra A 1, considered as a Poisson version of the quantum generalized Weyl algebra, is constructed and its Poisson structures are studied. In particular, a necessary and sufficient condition is obtained, such that A 1 is Poisson simple and established that the Poisson endomorphisms of A 1 are Poisson analogues of the endomorphisms of the quantum generalized Weyl algebra.

Concurrently coupled numerical simulations using heterogeneous solvers are powerful tools for modeling multiscale phenomena. However, major modifications to existing codes are often required to enable such simulations, posing significant difficulties in practice. In this paper we present a C++ library, i.e. the Multiscale Universal Interface (MUI), which is capable of facilitating the coupling effort for a wide range of multiscale simulations. The library adopts a header-only form with minimal external dependency and hence can be easily dropped into existing codes. A data sampler concept is introduced, combined with a hybrid dynamic/static typing mechanism, to create an easily customizable framework for solver-independent data interpretation. The library integrates MPI MPMD support and an asynchronous communication protocol to handle inter-solver information exchange irrespective of the solvers' own MPI awareness. Template metaprogramming is heavily employed to simultaneously improve runtime performance and code flexibility. We validated the library by solving three different multiscale problems, which also serve to demonstrate the flexibility of the framework in handling heterogeneous models and solvers. In the first example, a Couette flow was simulated using two concurrently coupled Smoothed Particle Hydrodynamics (SPH) simulations of different spatial resolutions. In the second example, we coupled the deterministic SPH method with the stochastic Dissipative Particle Dynamics (DPD) method to study the effect of surface grafting on the hydrodynamics properties on the surface. In the third example, we consider conjugate heat transfer between a solid domain and a fluid domain by coupling the particle-based energy-conserving DPD (eDPD) method with the Finite Element Method (FEM).

Graphical abstract: - Abstract: Concurrently coupled numerical simulations using heterogeneous solvers are powerful tools for modeling multiscale phenomena. However, major modifications to existing codes are often required to enable such simulations, posing significant difficulties in practice. In this paper we present a C++ library, i.e. the Multiscale Universal Interface (MUI), which is capable of facilitating the coupling effort for a wide range of multiscale simulations. The library adopts a header-only form with minimal external dependency and hence can be easily dropped into existing codes. A data sampler concept is introduced, combined with a hybrid dynamic/static typing mechanism, to create an easily customizable framework for solver-independent data interpretation. The library integrates MPI MPMD support and an asynchronous communication protocol to handle inter-solver information exchange irrespective of the solvers' own MPI awareness. Template metaprogramming is heavily employed to simultaneously improve runtime performance and code flexibility. We validated the library by solving three different multiscale problems, which also serve to demonstrate the flexibility of the framework in handling heterogeneous models and solvers. In the first example, a Couette flow was simulated using two concurrently coupled Smoothed Particle Hydrodynamics (SPH) simulations of different spatial resolutions. In the second example, we coupled the deterministic SPH method with the stochastic Dissipative Particle Dynamics (DPD) method to study the effect of surface grafting on the hydrodynamics properties on the surface. In the third example, we consider conjugate heat transfer between a solid domain and a fluid domain by coupling the particle-based energy-conserving DPD (eDPD) method with the Finite Element Method (FEM)

This paper describes a new high performance implementation of the QR-based Dynamically Weighted Halley Singular Value Decomposition (QDWH-SVD) solver on multicore architecture enhanced with multiple GPUs. The standard QDWH-SVD algorithm was introduced by Nakatsukasa and Higham (SIAM SISC, 2013) and combines three successive computational stages: (1) the polar decomposition calculation of the original matrix using the QDWH algorithm, (2) the symmetric eigendecomposition of the resulting polar factor to obtain the singular values and the right singular vectors and (3) the matrix-matrix multiplication to get the associated left singular vectors. A comprehensive test suite highlights the numerical robustness of the QDWH-SVD solver. Although it performs up to two times more flops when computing all singular vectors compared to the standard SVD solver algorithm, our new high performance implementation on single GPU results in up to 3.8x improvements for asymptotic matrix sizes, compared to the equivalent routines from existing state-of-the-art open-source and commercial libraries. However, when only singular values are needed, QDWH-SVD is penalized by performing up to 14 times more flops. The singular value only implementation of QDWH-SVD on single GPU can still run up to 18% faster than the best existing equivalent routines. Integrating mixed precision techniques in the solver can additionally provide up to 40% improvement at the price of losing few digits of accuracy, compared to the full double precision floating point arithmetic. We further leverage the single GPU QDWH-SVD implementation by introducing the first multi-GPU SVD solver to study the scalability of the QDWH-SVD framework.

The area of software analysis, testing and verification is now undergoing a revolution thanks to the use of automated and scalable support for logical methods. A well-recognized premise is that at the core of software analysis engines is invariably a component using logical formulas for describing states and transformations between system states. The process of using this information for discovering and checking program properties (including such important properties as safety and security) amounts to automatic theorem proving. In particular, theorem provers that directly support common software constructs offer a compelling basis. Such provers are commonly called satisfiability modulo theories (SMT) solvers. Z3 is a state-of-the-art SMT solver. It is developed at Microsoft Research. It can be used to check the satisfiability of logical formulas over one or more theories such as arithmetic, bit-vectors, lists, records and arrays. The talk describes some of the technology behind modern SMT solvers, including the solver Z3. Z3 is currently mainly targeted at solving problems that arise in software analysis and verification. It has been applied to various contexts, such as systems for dynamic symbolic simulation (Pex, SAGE, Vigilante), for program verification and extended static checking (Spec#/Boggie, VCC, HAVOC), for software model checking (Yogi, SLAM), model-based design (FORMULA), security protocol code (F7), program run-time analysis and invariant generation (VS3). We will describe how it integrates support for a variety of theories that arise naturally in the context of the applications. There are several new promising avenues and the talk will touch on some of these and the challenges related to SMT solvers. Proceedings

Both necessity and opportunity motivate the use of high-performance computers for iterative linear solvers. Necessity results from the size of the problems being solved-smaller problems are often better handled by direct methods. Opportunity arises from the formulation of the iterative methods in terms of simple linear algebra operations, even if this {open_quote}natural{close_quotes} parallelism is not easy to exploit in irregularly structured sparse matrices and with good preconditioners. As a result, high-performance implementations of iterative solvers have attracted a lot of interest in recent years. Most efforts are geared to vectorize or parallelize the dominating operation-structured or unstructured sparse matrix-vector multiplication, or to increase locality and parallelism by reformulating the algorithm-reducing global synchronization in inner products or local data exchange in preconditioners. Target architectures for iterative solvers currently include mostly vector supercomputers and architectures with one or few optimized (e.g., super-scalar and/or super-pipelined RISC) processors and hierarchical memory systems. More recently, parallel computers with physically distributed memory and a better price/performance ratio have been offered by vendors as a very interesting alternative to vector supercomputers. However, programming comfort on such distributed memory parallel processors (DMPPs) still lags behind. Here the authors are concerned with iterative solvers and their changing computing environment. In particular, they are considering migration from traditional vector supercomputers to DMPPs. Application requirements force one to use flexible and portable libraries. They want to extend the portability of iterative solvers rather than reimplementing everything for each new machine, or even for each new architecture.

A new method is presented for solving Poisson's equation inside an open-ended rectangular pipe. The method uses Fast Fourier Transforms (FFTs)to perform mixed convolutions and correlations of the charge density with the Green function. Descriptions are provided for algorithms based on theordinary Green function and for an integrated Green function (IGF). Due to its similarity to the widely used Hockney algorithm for solving Poisson'sequation in free space, this capability can be easily implemented in many existing particle-in-cell beam dynamics codes.

Continuum modeling of electrostatic interactions based upon numerical solutions of the Poisson-Boltzmann equation has been widely used in structural and functional analyses of biomolecules. A limitation of the numerical strategies is that it is conceptually difficult to incorporate these types of models into molecular mechanics simulations, mainly because of the issue in assigning atomic forces. In this theoretical study, we first derived the Maxwell stress tensor for molecular systems obeying the full nonlinear Poisson-Boltzmann equation. We further derived formulations of analytical electrostatic forces given the Maxwell stress tensor and discussed the relations of the formulations with those published in the literature. We showed that the formulations derived from the Maxwell stress tensor require a weaker condition for its validity, applicable to nonlinear Poisson-Boltzmann systems with a finite number of singularities such as atomic point charges and the existence of discontinuous dielectric as in the widely used classical piece-wise constant dielectric models.

We consider a class of map, recently derived in the context of cluster mutation. In this paper we start with a brief review of the quiver context, but then move onto a discussion of a related Poisson bracket, along with the Poisson algebra of a special family of functions associated with these maps. A bi-Hamiltonian structure is derived and used to construct a sequence of Poisson commuting functions and hence show complete integrability. Canonical coordinates are derived, with the map now being a canonical transformation with a sequence of commuting invariant functions. Compatibility of a pair of these functions gives rise to Liouville's equation and the map plays the role of a B\\"acklund transformation.

We extend the coupling to the topological backgrounds, recently worked out for the 2-dimensional BF-model, to the most general Poisson sigma models. The coupling involves the choice of a Casimir function on the target manifold and modifies the BRST transformations. This in turn induces a change in the BRST cohomology of the resulting theory. The observables of the coupled theory are analyzed and their geometrical intrepretation is given. We finally couple the theory to 2-dimensional topological gravity: this is the first step to study a topological string theory in propagation on a Poisson manifold. As an application, we show that the gauge-fixed vectorial supersymmetry of the Poisson sigma models has a natural explanation in terms of the theory coupled to topological gravity.

A countable Markov chain in a Markovian environment is considered. A Poisson limit theorem for the chain recurring to small cylindrical sets is mainly achieved. In order to prove this theorem, the entropy function h is introduced and the Shannon-McMillan-Breiman theorem for the Markov chain in a Markovian environment is shown. It' s well-known that a Markov process in a Markovian environment is generally not a standard Markov chain, so an example of Poisson approximation for a process which is not a Markov process is given. On the other hand, when the environmental process degenerates to a constant sequence, a Poisson limit theorem for countable Markov chains, which is the generalization of Pitskel's result for finite Markov chains is obtained.

We extend the coupling to the topological backgrounds, recently worked out for the 2-dimensional BF-model, to the most general Poisson sigma models. The coupling involves the choice of a Casimir function on the target manifold and modifies the BRST transformations. This in turn induces a change in the BRST cohomology of the resulting theory. The observables of the coupled theory are analyzed and their geometrical interpretation is given. We finally couple the theory to 2-dimensional topological gravity: this is the first step to study a topological string theory in propagation on a Poisson manifold. As an application, we show that the gauge-fixed vectorial supersymmetry of the Poisson sigma models has a natural explanation in terms of the theory coupled to topological gravity.

We introduce an algorithm for the segmentation of a class of regime switching processes. The segmentation algorithm is a non parametric statistical method able to identify the regimes (patches) of the time series. The process is composed of consecutive patches of variable length, each patch being described by a stationary compound Poisson process, i.e. a Poisson process where each count is associated to a fluctuating signal. The parameters of the process are different in each patch and therefore the time series is non stationary. Our method is a generalization of the algorithm introduced by Bernaola-Galvan, et al., Phys. Rev. Lett., 87, 168105 (2001). We show that the new algorithm outperforms the original one for regime switching compound Poisson processes. As an application we use the algorithm to segment the time series of the inventory of market members of the London Stock Exchange and we observe that our method finds almost three times more patches than the original one.

We describe a new class of negative Poisson's ratio (NPR) open cell PU-PE foams produced by blocking the shape memory effect in the polymer. Contrary to classical NPR open cell thermoset and thermoplastic foams that return to their auxetic phase after reheating (and therefore limit their use in technological applications), this new class of cellular solids has a permanent negative Poisson's ratio behavior, generated through multiple shape memory (mSM) treatments that lead to a fixity of the topology of the cell foam. The mSM-NPR foams have Poisson's ratio values similar to the auxetic foams prior their return to the conventional phase, but compressive stress-strain curves similar to the ones of conventional foams. The results show that by manipulating the shape memory effect in polymer microstructures it is possible to obtain new classes of materials with unusual deformation mechanisms.

Time series of rainfall bucket tip times at the Beaufort Park station, Bracknell, in the UK are modelled by a class of Markov modulated Poisson processes (MMPP) which may be thought of as a generalization of the Poisson process. Our main focus in this paper is to investigate the effects of including covariate information into the MMPP model framework on statistical properties. In particular, we look at three types of time-varying covariates namely temperature, sea level pressure, and relative humidity that are thought to be affecting the rainfall arrival process. Maximum likelihood estimation is used to obtain the parameter estimates, and likelihood ratio tests are employed in model comparison. Simulated data from the fitted model are used to make statistical inferences about the accumulated rainfall in the discrete time interval. Variability of the daily Poisson arrival rates is studied.

The link between (super)-affine Lie algebras as Poisson brackets structures and integrable hierarchies provides both a classification and a tool for obtaining superintegrable hierarchies. The lack of a fully systematic procedure for constructing matrix-type Lax operators, which makes the supersymmetric case essentially different from the bosonic counterpart, is overcome via the notion of Poisson embeddings (P.E.), i.e. Poisson mappings relating affine structures to conformal structures (in their simplest version P.E. coincide with the Sugawara construction). A full class of hierarchies can be recovered by using uniquely Lie-algebraic notions. The group-algebraic properties implicit in the super-affine picture allow a systematic derivation of reduced hierarchies by imposing either coset conditions or hamiltonian constraints (or possibly both).

Full Text Available An algorithm for generating equivalent Poisson packet traffic based on empirical traffic data is presented in this paper. Two steps are required in order to produce equivalent Poisson packet traffic. Real traffic trace is analyzed in the first step. In the second step, a new equivalent synthetic Poisson traffic is generated in such a way that the first order statistical parameters remain unchanged. New packet inter-arrival time series are produced in a random manner using negative exponential probability distribution with a known mean. New packet size series are also produced in a random manner. However, due to specified minimum and maximum packet sizes, a truncated exponential probability distribution is applied.

We present a detailed derivation of the master equation describing a general time-dependent quantum system with classical Poisson white noise and outline its various properties. We discuss the limiting cases of Poisson white noise and provide approximations for the different noise strength regimes. We show that using the eigenstates of the noise superoperator as a basis can be a useful way of expressing the master equation. Using this, we simulate various settings to illustrate different effects of Poisson noise. In particular, we show a dip in the fidelity as a function of noise strength where high fidelity can occur in the strong-noise regime for some cases. We also investigate recent claims [J. Jing et al., Phys. Rev. A 89, 032110 (2014), 10.1103/PhysRevA.89.032110] that this type of noise may improve rather than destroy adiabaticity.

Performance of nuclear threat detection systems based on gamma-ray spectrometry often strongly depends on the ability to identify the part of measured signal that can be attributed to background radiation. We have successfully applied a method based on Principal Component Analysis (PCA) to obtain a compact null-space model of background spectra using PCA projection residuals to derive a source detection score. We have shown the method's utility in a threat detection system using mobile spectrometers in urban scenes (Tandon et al 2012). While it is commonly assumed that measured photon counts follow a Poisson process, standard PCA makes a Gaussian assumption about the data distribution, which may be a poor approximation when photon counts are low. This paper studies whether and in what conditions PCA with a Poisson-based loss function (Poisson PCA) can outperform standard Gaussian PCA in modeling background radiation to enable more sensitive and specific nuclear threat detection.

We extend the coupling to the topological backgrounds, recently worked out for the 2-dimensional BF-model, to the most general Poisson sigma models. The coupling involves the choice of a Casimir function on the target manifold and modifies the BRST transformations. This in turn induces a change in the BRST cohomology of the resulting theory. The observables of the coupled theory are analyzed and their geometrical interpretation is given. We finally couple the theory to 2-dimensional topological gravity: this is the first step to study a topological string theory in propagation on a Poisson manifold. As an application, we show that the gauge-fixed vectorial supersymmetry of the Poisson sigma models has a natural explanation in terms of the theory coupled to topological gravity.

An efficient hydraulic optimization procedure, suitable for industrial use, requires an advanced optimization tool (EASY software), a fastsolver (block coupled CFD) and a flexible geometry generation tool. EASY optimization software is a PCA-driven metamodel-assisted Evolutionary Algorithm (MAEA (PCA)) that can be used in both single- (SOO) and multiobjective optimization (MOO) problems. In MAEAs, low cost surrogate evaluation models are used to screen out non-promising individuals during the evolution and exclude them from the expensive, problem specific evaluation, here the solution of Navier-Stokes equations. For additional reduction of the optimization CPU cost, the PCA technique is used to identify dependences among the design variables and to exploit them in order to efficiently drive the application of the evolution operators. To further enhance the hydraulic optimization procedure, a very robust and fast Navier-Stokes solver has been developed. This incompressible CFD solver employs a pressure-based block-coupled approach, solving the governing equations simultaneously. This method, apart from being robust and fast, also provides a big gain in terms of computational cost. In order to optimize the geometry of hydraulic machines, an automatic geometry and mesh generation tool is necessary. The geometry generation tool used in this work is entirely based on b-spline curves and surfaces. In what follows, the components of the tool chain are outlined in some detail and the optimization results of hydraulic machine components are shown in order to demonstrate the performance of the presented optimization procedure.

A Poisson-Fermi model is proposed for calculating activity coefficients of single ions in strong electrolyte solutions based on the experimental Born radii and hydration shells of ions in aqueous solutions. The steric effect of water molecules and interstitial voids in the first and second hydration shells play an important role in our model. The screening and polarization effects of water are also included in the model that can thus describe spatial variations of dielectric permittivity, water density, void volume, and ionic concentration. The activity coefficients obtained by the Poisson-Fermi model with only one adjustable parameter are shown to agree with experimental data, which vary nonmonotonically with salt concentrations.

Consider the quasi-commutative approximation to a noncommutative geometry. It is shown that there is a natural map from the resulting Poisson structure to the Riemann curvature of a metric. This map is applied to the study of high-frequency gravitational radiation. In classical gravity in the WKB approximation there are two results of interest, a dispersion relation and a conservation law. Both of these results can be extended to the noncommutative case, with the difference that they result from a cocycle condition on the high-frequency contribution to the Poisson structure, not from the field equations. (orig.)

In this paper, we consider the simultaneous estimation of the parameters (means) of the independent Poisson distribution by using the following loss functions: L0(θ，T)=∑i=1n(Ti-θi)2，L1(θ，T)=∑i=1n(Ti-θi)2/θi We develop an estimator which is better than the maximum likelihood estimator X simultaneously under L0(θ, T) and L1(θ, T). Our estimator possesses substantially smaller risk than the usual estimator X to estimate the parameters (means) of the independent Poisson distribution.

We formulate Yang-Mills theory in terms of the large-N limit, viewed as a classical limit, of gauge-invariant dynamical variables, which are closely related to Wilson loops, via deformation quantization. We obtain a Poisson algebra of these dynamical variables corresponding to normal-ordered quantum (at a finite value of $\\hbar$) operators. Comparing with a Poisson algebra one of us introduced in the past for Weyl-ordered quantum operators, we find, using ideas closly related to topological g...

This paper investigates the ? filtering problem for stochastic systems driven by Poisson processes. By utilising the martingale theory such as the predictable projection operator and the dual predictable projection operator, this paper transforms the expectation of stochastic integral with respect to the Poisson process into the expectation of Lebesgue integral. Then, based on this, this paper designs an ? filter such that the filtering error system is mean-square asymptotically stable and satisfies a prescribed ? performance level. Finally, a simulation example is given to illustrate the effectiveness of the proposed filtering scheme.

Source localization problem for Poisson equation with available noisy boundary data is well known to be highly sensitive to noise. The problem is ill posed and lacks to fulfill Hadamards stability criteria for well posedness. In this work, first a robust iterative observer is presented for boundary estimation problem for Laplace equation, and then this algorithm along with the available noisy boundary data from the Poisson problem is used to localize point sources inside a rectangular domain. The algorithm is inspired from Kalman filter design, however one of the space variables is used as time-like. Numerical implementation along with simulation results is detailed towards the end.

The paper provides a simpler method for proving a delicate inequality that was used by Achlioptis and Naor to establish asymptotic concentration for chromatic numbers of Erdos-Renyi random graphs. The simplifications come from two new ideas. The first involves a sharpened form of a piece of statistical folklore regarding goodness-of-fit tests for two-way tables of Poisson counts under linear conditioning constraints. The second idea takes the form of a new inequality that controls the extreme tails of the distribution of a quadratic form in independent Poissons random variables.

Poisson-disk sampling is one of the fundamental research problems in computer graphics that has many applications. In this paper, we study the problem of maximal Poisson-disk sampling on mesh surfaces. We present a simple approach that generalizes the 2D maximal sampling framework to surfaces. The key observation is to use a subdivided mesh as the sampling domain for conflict checking and void detection. Our approach improves the state-of-the-art approach in efficiency, quality and the memory consumption.

The "double-cut-and-join" (DCJ) model of genome rearrangement proposed by Yancopoulos et al. uses the single DCJ operation to account for all genome rearrangement events. Given three signed permutations, the DCJ median problem is to find a fourth permutation that minimizes the sum of the pairwise DCJ distances between it and the three others. In this paper, we present a branch-and-bound method that provides accurate solution to the multichromosomal DCJ median problems. We conduct extensive simulations and the results show that the DCJ median solver performs better than other median solvers for most of the test cases. These experiments also suggest that DCJ model is more suitable for real datasets where both reversals and transpositions occur.

The increasing gap between processor performance and memory access time warrants the re-examination of data movement in iterative linear solver algorithms. For this reason, we explore and establish the feasibility of modifying a standard iterative linear solver algorithm in a manner that reduces the movement of data through memory. In particular, we present an alternative to the restarted GMRES algorithm for solving a single right-hand side linear system Ax = b based on solving the block linear system AX = B. Algorithm performance, i.e. time to solution, is improved by using the matrix A in operations on groups of vectors. Experimental results demonstrate the importance of implementation choices on data movement as well as the effectiveness of the new method on a variety of problems from different application areas.

An open problem that arises when using modern iterative linear solvers, such as the preconditioned conjugate gradient (PCG) method or Generalized Minimum RESidual method (GMRES) is how to choose the residual tolerance in the linear solver to be consistent with the tolerance on the solution error. This problem is especially acute for integrated groundwater models which are implicitly coupled to another model, such as surface water models, and resolve both multiple scales of flow and temporal interaction terms, giving rise to linear systems with variable scaling. This article uses the theory of 'forward error bound estimation' to show how rescaling the linear system affects the correspondence between the residual error in the preconditioned linear system and the solution error. Using examples of linear systems from models developed using the USGS GSFLOW package and the California State Department of Water Resources' Integrated Water Flow Model (IWFM), we observe that this error bound guides the choice of a prac...

We have developed infrastructure, utilities and partitioning methods to improve data partitioning in linear solvers and preconditioners. Our efforts included incorporation of data repartitioning capabilities from the Zoltan toolkit into the Trilinos solver framework, (allowing dynamic repartitioning of Trilinos matrices); implementation of efficient distributed data directories and unstructured communication utilities in Zoltan and Trilinos; development of a new multi-constraint geometric partitioning algorithm (which can generate one decomposition that is good with respect to multiple criteria); and research into hypergraph partitioning algorithms (which provide up to 56% reduction of communication volume compared to graph partitioning for a number of emerging applications). This report includes descriptions of the infrastructure and algorithms developed, along with results demonstrating the effectiveness of our approaches.

We present a family of scalable preconditioners for matrices arising in the discretization of $H(div)$ problems using the lowest order Raviart--Thomas finite elements. Our approach belongs to the class of “auxiliary space''--based methods and requires only the finite element stiffness matrix plus some minimal additional discretization information about the topology and orientation of mesh entities. Also, we provide a detailed algebraic description of the theory, parallel implementation, and different variants of this parallel auxiliary space divergence solver (ADS) and discuss its relations to the Hiptmair--Xu (HX) auxiliary space decomposition of $H(div)$ [SIAM J. Numer. Anal., 45 (2007), pp. 2483--2509] and to the auxiliary space Maxwell solver AMS [J. Comput. Math., 27 (2009), pp. 604--623]. Finally, an extensive set of numerical experiments demonstrates the robustness and scalability of our implementation on large-scale $H(div)$ problems with large jumps in the material coefficients.

In the magnetosphere of a rotating black hole, an inner Alfven critical surface (IACS) must be crossed by inflowing plasma. Inside the IACS, Alfven waves are inward directed toward the black hole. The majority of the proper volume of the active region of spacetime (the ergosphere) is inside of the IACS. The charge and the totally transverse momentum flux (the momentum flux transverse to both the wave normal and the unperturbed magnetic field) are both determined exclusively by the Alfven polarization. However, numerical simulations of black hole magnetospheres are often based on 1-D HLL Riemann solvers that readily dissipate Alfven waves. Elements of the dissipated wave emerge in adjacent cells regardless of the IACS, there is no mechanism to prevent Alfvenic information from crossing outward. Thus, it is unclear how simulated magnetospheres attain the substantial Goldreich-Julian charge density associated with the rotating magnetic field. The HLL Riemann solver is also notorious for producing large recurring...

This paper documents the implementation of a distributive out-of-core (OOC) solver for performing LU and Cholesky factorizations of a large dense matrix on clusters of many-core programmable co-processors. The out-of- core algorithm combines both the left-looking and right-looking schemes aimed to minimize the movement of data between the CPU host and the co-processor, optimizing data locality as well as computing throughput. The OOC solver is built to align with the format of the ScaLAPACK software library, making it readily portable to any existing codes using ScaLAPACK. A runtime analysis conducted on Beacon (an Intel Xeon plus Intel Xeon Phi cluster which composed of 48 nodes of multi-core CPU and MIC) at the Na- tional Institute for Computational Sciences is presented. Comparison of the performance on the Intel Xeon Phi and GPU clusters are also provided.

Abstract Benchmarking of full-wave solvers for ICRF simulations is performed using plasma profiles and equilibria obtained from integrated self-consistent modeling predictions of four ITER plasmas. One is for a high performance baseline (5.3 T, 15 MA) DT H-mode. The others are for half-field, half-current plasmas of interest for the pre-activation phase with bulk plasma ion species being either hydrogen or He4. The predicted profiles are used by six full-wave solver groups to simulate the ICRF electromagnetic fields and heating, and by three of these groups to simulate the current-drive. Approximate agreement is achieved for the predicted heating power for the DT and He4 cases. Factor of two disagreements are found for the cases with second harmonic He3 heating in bulk H cases. Approximate agreement is achieved simulating the ICRF current drive.

Plasticity/Fracture and rock failure are essential ingredients in geodynamic models as terrestrial rocks do not possess an infinite yield strength. Numerous physical mechanisms have been proposed to limit the strength of rocks, including low temperature plasticity and brittle fracture. While ductile and creep behavior of rocks at depth is largely accepted, the constitutive relations associated with brittle failure, or shear localisation, are more controversial. Nevertheless, there are really only a few macroscopic constitutive laws for visco-plasticity that are regularly used in geodynamics models. Independent of derivation, all of these can be cast as simple effective viscosities which act as stress limiters with different choices for yield surfaces; the most common being a von Mises (constant yield stress) or Drucker-Prager (pressure dependent yield-stress) criterion. The choice of plasticity model, however, can have significant consequences for the degree of non-linearity in a problem and the choice and efficiency of non-linear solvers. Here we describe a series of simplified 2 and 3-D model problems to elucidate several issues associated with obtaining accurate description and solution of visco-plastic problems. We demonstrate that1) Picard/Successive substitution schemes for solution of the non-linear problems can often stall at large values of the non-linear residual, thus producing spurious solutions2) Combined Picard/Newton schemes can be effective for a range of plasticity models, however, they can produce serious convergence problems for strongly pressure dependent plasticity models such as Drucker-Prager.3) Nevertheless, full Drucker-Prager may not be the plasticity model of choice for strong materials as the dynamic pressures produced in these layers can develop pathological behavior with Drucker-Prager, leading to stress strengthening rather than stress weakening behavior.4) In general, for any incompressible Stoke's problem, it is highly advisable to

not for the PQN method. For the latter method the size of the active set is controlled to promote sparse solutions. This is described in Section 3.2.1...or any other aspect of this collection of information, including suggestions for reducing the burden, to Department of Defense, Washington...21005-5066 primary author’s email: <james.p.collins106.civ@mail.mil>. Parallel nonnegative least squares (NNLS) solvers are developed specifically for

Answer set programming (ASP) is a declarative programming formalism that allows a practitioner to specify a problem without describing an algorithm for solving it. In ASP, the tools for processing problem specifications are called answer set solvers. Because specified problems are often NP complete, these systems often require significant computational effort to succeed. Furthermore, they offer different heuristics, expose numerous parameters, and their running time is sensitive to the config...

An optimization problem can be characterized by an object-function, which is maximized, and restrictions, which limit the variation of the variables. A subclass of optimization is Linear Programming (LP), where both the object-function and the restrictions are linear functions of the variables. The traditional solution methods for LP problems are based on the simplex method, and it is customary to allow only non-negative variables. Compared to other optimization routines the LP solvers are more robust and the optimum is reached in a finite number of steps and is not sensitive to the starting point. For structural applications many optimization problems can be linearized and solved by LP routines. However, the structural variables are not always non-negative, and this requires a reformation, where a variable x is substituted by the difference of two non-negative variables, x(sup + ) and x(sup - ). The transformation causes a doubling of the number of variables, and in a computer implementation the memory allocation doubles and for a typical problem the execution time at least doubles. This paper describes a LP solver written in C, which can handle a combination of non-negative variables and unlimited variables. The LP solver also allows restart, and this may reduce the computational costs if the solution to a similar LP problem is known a priori. The algorithm is based on the simplex method, and differs only in the logical choices. Application of the new LP solver will at the same time give both a more direct problem formulation and a more efficient program.

Context. Chemistry often plays an important role in astrophysical gases. It regulates thermal properties by changing species abundances and via ionization processes. This way, time-dependent cooling mechanisms and other chemistry-related energy sources can have a profound influence on the dynamical evolution of an astrophysical system. Modeling those effects with the underlying chemical kinetics in realistic magneto-gasdynamical simulations provide the basis for a better link to observations. Aims: The present work describes the implementation of a chemical reaction network solver into the magneto-gasdynamical code NIRVANA. For this purpose a multispecies structure is installed, and a new module for evolving the rate equations of chemical kinetics is developed and coupled to the dynamical part of the code. A small chemical network for a hydrogen-helium plasma was constructed including associated thermal processes which is used in test problems. Methods: Evolving a chemical network within time-dependent simulations requires the additional solution of a set of coupled advection-reaction equations for species and gas temperature. Second-order Strang-splitting is used to separate the advection part from the reaction part. The ordinary differential equation (ODE) system representing the reaction part is solved with a fourth-order generalized Runge-Kutta method applicable for stiff systems inherent to astrochemistry. Results: A series of tests was performed in order to check the correctness of numerical and technical implementation. Tests include well-known stiff ODE problems from the mathematical literature in order to confirm accuracy properties of the solver used as well as problems combining gasdynamics and chemistry. Overall, very satisfactory results are achieved. Conclusions: The NIRVANA code is now ready to handle astrochemical processes in time-dependent simulations. An easy-to-use interface allows implementation of complex networks including thermal processes

The aims of this paper are threefold: to increase the level of awareness within the shock capturing community to the fact that many Godunov-type methods contain subtle flaws that can cause spurious solutions to be computed; to identify one mechanism that might thwart attempts to produce very high resolution simulations; and to proffer a simple strategy for overcoming the specific failings of individual Riemann solvers.

Based on constructing programmed constraint and constraint perturbation equation, a kinematics and dynamics numerical simulation model is established for virtual mechanism, in which the difference scheme guarantee precision in simulation procedure and its numerical solutions satisfy programmed manifold stability. A crank-piston mechanism in a car engine, a steering mechanism and a suspension mechanism are simulated in a virtual environment, then comparing the simulation results with those obtained in ADAMS under the same circumstances proved the solver valid.

The stability question of the Lane-Emden stationary gaseous star configurations is an interesting problem arising in astrophysics. We establish both linear and nonlinear dynamical instability results for the Lane-Emden solutions in the framework of the Navier-Stokes-Poisson system with adiabatic exponent $6/5 < \\gamma < 4/3$.

In this note,we present a framework for the large time behavior of general uniformly bounded weak entropy solutions to the Cauchy problem of Euler-Poisson system of semiconductor devices.It is shown that the solutions converges to the stationary solutions exponentially in time.No smallness and regularity conditions are assumed.

Graphene can be made auxetic through the introduction of vacancy defects. This results in the thinnest negative Poisson's ratio material at ambient conditions known so far, an effect achieved via a nanoscale de-wrinkling mechanism that mimics the behavior at the macroscale exhibited by a crumpled sheet of paper when stretched.

Variational methods are used to study the nonlinear Schr(o)dinger-Poisson type equations which model the electromagnetic wave propagating in the plasma in physics. By analyzing the Halniltonian property to construct a constrained variational problem, the existence of the ground state of the system is obtained. Furthermore, it is shown that the ground state is orbitally stable.

We construct a new supermatrix model which represents a manifestly supersymmetric noncommutative regularisation of the UOSp(2|1) supersymmetric Schwinger model on the supersphere. Our construction is much simpler than those already existing in the literature and it was found by using Poisson geometry in a substantial way.

A pair of conformal sigma models related by Poisson-Lie T-duality is constructed by starting with the O(2,2) Drinfeld double. The duality relates the standard SL(2,R) WZNW model to a constrained sigma model defined on SL(2,R) group space. The quantum equivalence of the models is established by using a path integral argument.

We develop a class of Poisson autoregressive models with additional covariates (PARX) that can be used to model and forecast time series of counts. We establish the time series properties of the models, including conditions for stationarity and existence of moments. These results are in turn used...

Full Text Available The Hardy type class of complex functions with infinite many variables defined on the Schrodinger irreducible unitary orbit of reduced Heisenberg group, generated by the Gauss density, is investigated. A Poisson integral type formula for their analytic extensions on an open ball is established. Taylor coefficients for analytic extensions are described by the associatedsymmetric Fock space.

We point out that a certain finite size effect in heavy ion physics, the canonical enhancement, is based on the difference of conservation constrained pair statistics for Poisson and Gauss distributions, respectively. Consequently it should occur in a wide range of phenomena, whenever comparing rare and frequent events.

Full Text Available When modelling count data that comes in the form of a time series, the static Poisson regression and standard time series models are often not appropriate. A current study therefore involves the evaluation of several observation-driven and parameter...

In this paper we provide theoretical support for the so-called "Sigmoidal Gaussian Cox Process" approach to learning the intensity of an inhomogeneous Poisson process on a d-dimensional domain. This method was proposed by Adams, Murray and MacKay (ICML, 2009), who developed a tractable computational

Full Text Available In this article we show that the Vlasov-Poisson system has a unique weak solution in the space $L_1cap L_infty$. For this purpose, we use the method of characteristics, unlike the approach in [12].

In this paper we provide theoretical support for the so-called "Sigmoidal Gaussian Cox Process" approach to learning the intensity of an inhomogeneous Poisson process on a d-dimensional domain. This method was proposed by Adams, Murray and MacKay (ICML, 2009), who developed a tractable computational

Given a sample from a discretely observed multidimensional compound Poisson process, we study the problem of nonparametric estimation of its jump size density r0 and intensity λ0. We take a nonparametric Bayesian approach to the problem and determine posterior contraction rates in this context, whic

Argues that the gamma mixture of Poisson processes, for all its perceived defects, can be used to make predictions regarding future library book circulations of a quality adequate for general management requirements. The use of the model is extensively illustrated with data from two academic libraries. (Nine references) (CLB)

We give an expression for the perturbed evolution of a free evolution by gentle, possibly velocity dependent, potential, in terms of the expectation with respect to a Poisson process on a group. Various applications are given in particular to usual quantum mechanics but also to Fermi and spin systems.

We give an expression for the perturbed evolution of a free evolution by gentle, possibly velocity dependent, potential, in terms of the expectation with respect to a Poisson process on a group. Various applications are given in particular to usual quantum mechanics but also to Fermi and spin systems.

Network arrivals are often modeled as Poisson processes for analytic simplicity, even though a number of traffic studies have shown that packet interarrivals are not exponentially distributed. The authors evaluate 21 wide-area traces, investigating a number of wide-area TCP arrival processes (session and connection arrivals, FTPDATA connection arrivals within FTP sessions, and TELNET packet arrivals) to determine the error introduced by modeling them using Poisson processes. The authors find that user-initiated TCP session arrivals, such as remote-login and file-transfer, are well-modeled as Poisson processes with fixed hourly rates, but that other connection arrivals deviate considerably from Poisson; that modeling TELNET packet interarrivals as exponential grievously underestimates the burstiness of TELNET traffic, but using the empirical Tcplib[DJCME92] interarrivals preserves burstiness over many time scales; and that FTPDATA connection arrivals within FTP sessions come bunched into ``connection bursts``, the largest of which are so large that they completely dominate FTPDATA traffic. Finally, they offer some preliminary results regarding how the findings relate to the possible self-similarity of wide-area traffic.

A three-dimensional family of solutions of the Jacobi equations for Poisson systems is characterized. In spite of its general form it is possible the explicit and global determination of its main features, such as the symplectic structure and the construction of the Darboux canonical form. Examples are given.

Owing to the stochastic nature of discrete processes such as photon counts in imaging, real-world data measurements often exhibit heteroscedastic behavior. In particular, time series components and other measurements may frequently be assumed to be non-iid Poisson random variables, whose rate parameter is proportional to the underlying signal of interest-witness literature in digital communications, signal processing, astronomy, and magnetic resonance imaging applications. In this work, we show that certain wavelet and filterbank transform coefficients corresponding to vector-valued measurements of this type are distributed as sums and differences of independent Poisson counts, taking the so-called Skellam distribution. While exact estimates rarely admit analytical forms, we present Skellam mean estimators under both frequentist and Bayes models, as well as computationally efficient approximations and shrinkage rules, that may be interpreted as Poisson rate estimation method performed in certain wavelet/filterbank transform domains. This indicates a promising potential approach for denoising of Poisson counts in the above-mentioned applications.

There is a concern in the computational fluid dynamics community that mesh generation is a significant bottleneck in the CFD workflow. This is one of several papers that will help set the stage for a moderated panel discussion addressing this issue. Although certain general "rules of thumb" and a priori mesh metrics can be used to ensure that some base level of mesh quality is achieved, inadequate consideration is often given to the type of solver or particular flow regime on which the mesh will be utilized. This paper explores how an analyst may want to think differently about a mesh based on considerations such as if a flow is compressible vs. incompressible or hypersonic vs. subsonic or if the solver is node-centered vs. cell-centered. This paper is a high-level investigation intended to provide general insight into how considering the nature of the solver or flow when performing mesh generation has the potential to increase the accuracy and/or robustness of the solution and drive the mesh generation process to a state where it is no longer a hindrance to the analysis process.

We analyse the performance of direct solvers when applied to a system of linear equations arising from an hh-adapted, C0C0 finite element space. Theoretical estimates are derived for typical hh-refinement patterns arising as a result of a point, edge, or face singularity as well as boundary layers. They are based on the elimination trees constructed specifically for the considered grids. Theoretical estimates are compared with experiments performed with MUMPS using the nested-dissection algorithm for construction of the elimination tree from METIS library. The numerical experiments provide the same performance for the cases where our trees are identical with those constructed by the nested-dissection algorithm, and worse performance for some cases where our trees are different. We also present numerical experiments for the cases with mixed singularities, where how to construct optimal elimination trees is unknown. In all analysed cases, the use of hh-adaptive grids significantly reduces the cost of the direct solver algorithm per unknown as compared to uniform grids. The theoretical estimates predict and the experimental data confirm that the computational complexity is linear for various refinement patterns. In most cases, the cost of the direct solver per unknown is lower when employing anisotropic refinements as opposed to isotropic ones.

The paper introduces a nonlinear multigrid solver for mixed nite element discretizations based on the Full Approximation Scheme (FAS) and element-based Algebraic Multigrid (AMGe). The main motivation to use FAS for unstruc- tured problems is the guaranteed approximation property of the AMGe coarse spaces that were developed recently at Lawrence Livermore National Laboratory. These give the ability to derive stable and accurate coarse nonlinear discretization problems. The previous attempts (including ones with the original AMGe method, [5, 11]), were less successful due to lack of such good approximation properties of the coarse spaces. With coarse spaces with approximation properties, our FAS approach on un- structured meshes should be as powerful/successful as FAS on geometrically re ned meshes. For comparison, Newton's method and Picard iterations with an inner state-of-the-art linear solver is compared to FAS on a nonlinear saddle point problem with applications to porous media ow. It is demonstrated that FAS is faster than Newton's method and Picard iterations for the experiments considered here. Due to the guaranteed approximation properties of our AMGe, the coarse spaces are very accurate, providing a solver with the potential for mesh-independent convergence on general unstructured meshes.

The Extreme Light Infrastructure (ELI) is expected to deliver peak intensities of 1023 - 1024 W/cm2 allowing to probe nonlinear Quantum Electrodynamics (QED) phenomena in an unprecedented regime. Within the framework of QED, the second order process of photon-photon scattering leads to a set of extended Maxwell's equations [W. Heisenberg and H. Euler, Z. Physik 98, 714] effectively creating nonlinear polarization and magnetization terms that account for the nonlinear response of the vacuum. To model this in a self-consistent way, we present a multi dimensional generalized Maxwell equation finite difference solver with significantly enhanced dispersive properties, which was implemented in the OSIRIS particle-in-cell code [R.A. Fonseca et al. LNCS 2331, pp. 342-351, 2002]. We present a detailed numerical analysis of this electromagnetic solver. As an illustration of the properties of the solver, we explore several examples in extreme conditions. We confirm the theoretical prediction of vacuum birefringence of a pulse propagating in the presence of an intense static background field [arXiv:1301.4918 [quant-ph

Newton iterative methods, also known as truncated Newton methods, are implementations of Newton`s method in which the linear systems that characterize Newton steps are solved approximately using iterative linear algebra methods. Here, we outline a well-developed Newton iterative algorithm together with a Fortran implementation called NITSOL. The basic algorithm is an inexact Newton method globalized by backtracking, in which each initial trial step is determined by applying an iterative linear solver until an inexact Newton criterion is satisfied. In the implementation, the user can specify inexact Newton criteria in several ways and select an iterative linear solver from among several popular {open_quotes}transpose-free{close_quotes} Krylov subspace methods. Jacobian-vector products used by the Krylov solver can be either evaluated analytically with a user-supplied routine or approximated using finite differences of function values. A flexible interface permits a wide variety of preconditioning strategies and allows the user to define a preconditioner and optionally update it periodically. We give details of these and other features and demonstrate the performance of the implementation on a representative set of test problems.

The aim of this work is to design and study a Balancing Domain Decomposition by Constraints (BDDC) solver for the nonlinear elasticity system modeling the mechanical deformation of cardiac tissue. The contraction–relaxation process in the myocardium is induced by the generation and spread of the bioelectrical excitation throughout the tissue and it is mathematically described by the coupling of cardiac electro-mechanical models consisting of systems of partial and ordinary differential equations. In this study, the discretization of the electro-mechanical models is performed by Q1 finite elements in space and semi-implicit finite difference schemes in time, leading to the solution of a large-scale linear system for the bioelectrical potentials and a nonlinear system for the mechanical deformation at each time step of the simulation. The parallel mechanical solver proposed in this paper consists in solving the nonlinear system with a Newton-Krylov-BDDC method, based on the parallel solution of local mechanical problems and a coarse problem for the so-called primal unknowns. Three-dimensional parallel numerical tests on different machines show that the proposed parallel solver is scalable in the number of subdomains, quasi-optimal in the ratio of subdomain to mesh sizes, and robust with respect to tissue anisotropy.

The Department of Energy (DOE) uses illness and injury surveillance to monitor morbidity and assess the overall health of the work force. Data collected from each participating site include health events and a roster file with demographic information. The source data files are maintained in a relational data base, and are used to obtain stratified tables of health event counts and person time at risk that serve as the starting point for Poisson regression analysis. The explanatory variables that define these tables are age, gender, occupational group, and time. Typical response variables of interest are the number of absences due to illness or injury, i.e., the response variable is a count. Poisson regression methods are used to describe the effect of the explanatory variables on the health event rates using a log-linear main effects model. Results of fitting the main effects model are summarized in a tabular and graphical form and interpretation of model parameters is provided. An analysis of deviance table is used to evaluate the importance of each of the explanatory variables on the event rate of interest and to determine if interaction terms should be considered in the analysis. Although Poisson regression methods are widely used in the analysis of count data, there are situations in which over-dispersion occurs. This could be due to lack-of-fit of the regression model, extra-Poisson variation, or both. A score test statistic and regression diagnostics are used to identify over-dispersion. A quasi-likelihood method of moments procedure is used to evaluate and adjust for extra-Poisson variation when necessary. Two examples are presented using respiratory disease absence rates at two DOE sites to illustrate the methods and interpretation of the results. In the first example the Poisson main effects model is adequate. In the second example the score test indicates considerable over-dispersion and a more detailed analysis attributes the over-dispersion to extra-Poisson

This report describes the numerical procedure used to implement the Green`s function method for solving the Poisson equation in two-dimensional Cartesian coordinates. The procedure can determine the solution to a problem with any or all of applied voltage boundary conditions, dielectric media, floating (insulated) conducting media, dielectric surface charging, periodic (reflective) boundary conditions, and volumetric space charge. The numerical solution is reasonably fast, and the dimension of the linear problem to be solved is that of the number of elements needed to represent the surfaces, not the whole computational volume. The method of solution is useful in the simulation of plasma particle motion in the vicinity of complex surface structures as found in microelectronics plasma processing applications. A FORTRAN implementation of this procedure is available from the author.

Doubly stochastic Poisson processes, also known as the Cox processes, frequently occur in various scientific fields. In this article, motivated primarily by analyzing Cox process data in biophysics, we propose a nonparametric kernel-based inference method. We conduct a detailed study, including an asymptotic analysis, of the proposed method, and provide guidelines for its practical use, introducing a fast and stable regression method for bandwidth selection. We apply our method to real photon arrival data from recent single-molecule biophysical experiments, investigating proteins' conformational dynamics. Our result shows that conformational fluctuation is widely present in protein systems, and that the fluctuation covers a broad range of time scales, highlighting the dynamic and complex nature of proteins' structure.

Here, we present a novel method for the solution of the diffusion equation on a composite AMR mesh. This approach is suitable for including diffusion based physics modules to hydrocodes that support ALE and AMR capabilities. To illustrate, we proffer our implementations of diffusion based radiation transport and heat conduction in a hydrocode called ALE-AMR. Numerical experiments conducted with the diffusion solver and associated physics packages yield 2nd order convergence in the L2 norm.

) for the Poisson distribution is also well known, but has not become generally used. This is primarily because, in contrast to non-linear least squares fitting, there has been no quick, robust, and general fitting method. In the field of fluorescence lifetime spectroscopy and imaging, there have been some efforts to use this estimator through minimization routines such as Nelder-Mead optimization, exhaustive line searches, and Gauss-Newton minimization. Minimization based on specific one- or multi-exponential models has been used to obtain quick results, but this procedure does not allow the incorporation of the instrument response, and is not generally applicable to models found in other fields. Methods for using the MLE for Poisson-distributed data have been published by the wider spectroscopic community, including iterative minimization schemes based on Gauss-Newton minimization. The slow acceptance of these procedures for fitting event counting histograms may also be explained by the use of the ubiquitous, fast Levenberg-Marquardt (L-M) fitting procedure for fitting non-linear models using least squares fitting (simple searches obtain {approx}10000 references - this doesn't include those who use it, but don't know they are using it). The benefits of L-M include a seamless transition between Gauss-Newton minimization and downward gradient minimization through the use of a regularization parameter. This transition is desirable because Gauss-Newton methods converge quickly, but only within a limited domain of convergence; on the other hand the downward gradient methods have a much wider domain of convergence, but converge extremely slowly nearer the minimum. L-M has the advantages of both procedures: relative insensitivity to initial parameters and rapid convergence. Scientists, when wanting an answer quickly, will fit data using L-M, get an answer, and move on. Only those that are aware of the bias issues will bother to fit using the more appropriate MLE

A robust and general solver for the radial Schrödinger, Dirac, and Kohn-Sham equations is presented. The formulation admits general potentials and meshes: uniform, exponential, or other defined by nodal distribution and derivative functions. For a given mesh type, convergence can be controlled systematically by increasing the number of grid points. Radial integrations are carried out using a combination of asymptotic forms, Runge-Kutta, and implicit Adams methods. Eigenfunctions are determined by a combination of bisection and perturbation methods for robustness and speed. An outward Poisson integration is employed to increase accuracy in the core region, allowing absolute accuracies of 10-8 Hartree to be attained for total energies of heavy atoms such as uranium. Detailed convergence studies are presented and computational parameters are provided to achieve accuracies commonly required in practice. Comparisons to analytic and current-benchmark density-functional results for atomic number Z=1-92 are presented, verifying and providing a refinement to current benchmarks. An efficient, modular Fortran 95 implementation, dftatom, is provided as open source, including examples, tests, and wrappers for interface to other languages; wherein particular emphasis is placed on the independence (no global variables), reusability, and generality of the individual routines. Program summaryProgram title:dftatom Catalogue identifier: AEPA_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEPA_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: MIT license No. of lines in distributed program, including test data, etc.: 14122 No. of bytes in distributed program, including test data, etc.: 157453 Distribution format: tar.gz Programming language: Fortran 95 with interfaces to Python and C. Computer: Any computer with a Fortran 95 compiler. Operating system: Any OS with a Fortran 95 compiler. RAM: 500 MB

Computation of first-arrival traveltimes for quasi-P waves in the presence of anisotropy is important for high-end near-surface modeling, microseismic-source localization, and fractured-reservoir characterization - and it requires solving an anisotropic eikonal equation. Anisotropy deviating from elliptical anisotropy introduces higher order nonlinearity into the eikonal equation, which makes solving the eikonal equation a challenge. We addressed this challenge by iteratively solving a sequence of simpler tilted elliptically anisotropic eikonal equations. At each iteration, the source function was updated to capture the effects of the higher order nonlinear terms. We used Aitken\\'s extrapolation to speed up convergence rate of the iterative algorithm. The result is an algorithm for computing first-arrival traveltimes in tilted anisotropic media. We evaluated the applicability and usefulness of our method on tilted transversely isotropic media and tilted orthorhombic media. Our numerical tests determined that the proposed method matches the first arrivals obtained by wavefield extrapolation, even for strongly anisotropic and highly complex subsurface structures. Thus, for the cases where two-point ray tracing fails, our method can be a potential substitute for computing traveltimes. The approach presented here can be easily extended to compute first-arrival traveltimes for anisotropic media with lower symmetries, such as monoclinic or even the triclinic media.

A variety of problems in device and materials design require the rapid forward modeling of Maxwell's equations in complex micro-structured materials. By combining high-order accurate integral equation methods with classical multiple scattering theory, we have created an effective simulation tool for materials consisting of an isotropic background in which are dispersed a large number of micro- or nano-scale metallic or dielectric inclusions.

Computing first-arrival traveltimes of quasi-P waves in the presence of anisotropy is important for high-end near-surface modeling, microseismic-source localization, and fractured-reservoir characterization, and requires solving an anisotropic eikonal equation. Anisotropy deviating from elliptical anisotropy introduces higher-order nonlinearity into the eikonal equation, which makes solving the eikonal equation a challenge. We address this challenge by iteratively solving a sequence of simpler tilted elliptically anisotropic eikonal equations. At each iteration, the source function is updated to capture the effects of the higher order nonlinear terms. We use Aitken extrapolation to speed up the convergence rate of the iterative algorithm. The result is an algorithm for first-arrival traveltime computations in tilted anisotropic media. We demonstrate our method on tilted transversely isotropic media and tilted orthorhombic media. Our numerical tests demonstrate that the proposed method can match the first arrivals obtained by wavefield extrapolation, even for strong anisotropy and complex structures. Therefore, for the cases where oneor two-point ray tracing fails, our method may be a potential substitute for computing traveltimes. Our approach can be extended to anisotropic media with lower symmetries, such as monoclinic or even triclinic media.

The aim of this paper is to present the stochastic Poisson equations associated to Lie algebroids. The stochastic Poisson equations associated to a refinement of a concrete principal bundle are determined.

Recantly, William Crawley-Boevey proposed the definition of a Poisson structure on a noncommutative algebra $A$ based on the Kontsevich principle. His idea was to find the {\\it weakest} possible structure on $A$ that induces standard (commutative) Poisson structures on all representation spaces $ \\Rep_V(A) $. It turns out that such a weak Poisson structure on $A$ is a Lie algebra bracket on the 0-th cyclic homology $ \\HC_0(A) $ satisfying some extra conditions; it was thus called in an {\\it $ H_0$-Poisson structure}. This paper studies a higher homological extension of this construction. In our more general setting, we show that noncommutative Poisson structures in the above sense behave nicely with respect to homotopy (in the sense that homotopy equivalent NC Poisson structures on $A$ induce (via the derived representation functor) homotopy equivalent Poisson algebra structures on the derved representation schemes $\\DRep_V(A) $). For an ordinary algebra $A$, a noncommutative Poisson structure on a semifree (...

The goal of this paper is to motivate the application of the recent numerical scheme called Fast Explicit Diffusion (FED) to solve long-term parabolic problems. With the purpose of performing long integration times the FED method is a simple and fast explicit solver, which has been introduced in the field of image processing. We show that FED is at least as fast as standard implicit methods, often has comparable or even better accuracy and is much easier to implement.

We construct a two-dimensional topological sigma model whose target space is endowed with a Poisson algebra for differential forms. The model consists of an equal number of bosonic and fermionic fields of worldsheet form degrees zero and one. The action is built using exterior products and derivatives, without any reference to a worldsheet metric, and is of the covariant Hamiltonian form. The equations of motion define a universally Cartan integrable system. In addition to gauge symmetries, the model has one rigid nilpotent supersymmetry corresponding to the target space de Rham operator. The rigid and local symmetries of the action, respectively, are equivalent to the Poisson bracket being compatible with the de Rham operator and obeying graded Jacobi identities. We propose that perturbative quantization of the model yields a covariantized differential star product algebra of Kontsevich type. We comment on the resemblance to the topological A model.

We construct a two-dimensional topological sigma model whose target space is endowed with a Poisson algebra for differential forms. The model consists of an equal number of bosonic and fermionic fields of worldsheet form degrees zero and one. The action is built using exterior products and derivatives, without any reference to any worldsheet metric, and is of the covariant Hamiltonian form. The equations of motion define a universally Cartan integrable system. In addition to gauge symmetries, the model has one rigid nilpotent supersymmetry corresponding to the target space de Rham operator. The rigid and local symmetries of the action, respectively, are equivalent to the Poisson bracket being compatible with the de Rham operator and obeying graded Jacobi identities. We propose that perturbative quantization of the model yields a covariantized differential star product algebra of Kontsevich type. We comment on the resemblance to the topological A model.

We introduce here the concept of Bayesian networks, in compound Poisson model, which provides a graphical modeling framework that encodes the joint probability distribution for a set of random variables within a directed acyclic graph. We suggest an approach proposal which offers a new mixed implicit estimator. We show that the implicit approach applied in compound Poisson model is very attractive for its ability to understand data and does not require any prior information. A comparative study between learned estimates given by implicit and by standard Bayesian approaches is established. Under some conditions and based on minimal squared error calculations, we show that the mixed implicit estimator is better than the standard Bayesian and the maximum likelihood estimators. We illustrate our approach by considering a simulation study in the context of mobile communication networks.

We construct a two-dimensional topological sigma model whose target space is endowed with a Poisson algebra for differential forms. The model consists of an equal number of bosonic and fermionic fields of worldsheet form degrees zero and one. The action is built using exterior products and derivatives, without any reference to a worldsheet metric, and is of the covariant Hamiltonian form. The equations of motion define a universally Cartan integrable system. In addition to gauge symmetries, the model has one rigid nilpotent supersymmetry corresponding to the target space de Rham operator. The rigid and local symmetries of the action, respectively, are equivalent to the Poisson bracket being compatible with the de Rham operator and obeying graded Jacobi identities. We propose that perturbative quantization of the model yields a covariantized differential star product algebra of Kontsevich type. We comment on the resemblance to the topological A model.

The POISSON/SUPERFISH Group codes were set up to solve two separate problems: the design of magnets and the design of rf cavities in a two-dimensional geometry. The first stage of either problem is to describe the layout of the magnet or cavity in a way that can be used as input to solve the generalized Poisson equation for magnets or the Helmholtz equations for cavities. The computer codes require that the problems be discretized by replacing the differentials (dx,dy) by finite differences ({delta}X,{delta}Y). Instead of defining the function everywhere in a plane, the function is defined only at a finite number of points on a mesh in the plane.

Random tessellations of the space represent a class of prototype models of heterogeneous media, which are central in several applications in physics, engineering, and life sciences. In this work, we investigate the statistical properties of d -dimensional isotropic Poisson geometries by resorting to Monte Carlo simulation, with special emphasis on the case d =3 . We first analyze the behavior of the key features of these stochastic geometries as a function of the dimension d and the linear size L of the domain. Then, we consider the case of Poisson binary mixtures, where the polyhedra are assigned two labels with complementary probabilities. For this latter class of random geometries, we numerically characterize the percolation threshold, the strength of the percolating cluster, and the average cluster size.

We derive the explicit form of the superpropagators in presence of general boundary conditions (coisotropic branes) for the Poisson Sigma Model. This generalizes the results presented in Cattaneo and Felder's previous works for the Kontsevich angle function used in the deformation quantization program of Poisson manifolds without branes or with at most two branes. The relevant superpropagators for n branes are defined as gauge fixed homotopy operators of a complex of differential forms on n sided polygons P_n with particular "alternating" boundary conditions. In presence of more than three branes we use first order Riemann theta functions with odd singular characteristics on the Jacobian variety of a hyperelliptic Riemann surface (canonical setting). In genus g the superpropagators present g zero modes contributions.

We study the Schr\\"odinger-Poisson system on the unit sphere $\\SS^2$ of $\\RR^3$, modeling the quantum transport of charged particles confined on a sphere by an external potential. Our first results concern the Cauchy problem for this system. We prove that this problem is regularly well-posed on every $H^s(\\SS ^2)$ with $s>0$, and not uniformly well-posed on $L^2(\\SS ^2)$. The proof of well-posedness relies on multilinear Strichartz estimates, the proof of ill-posedness relies on the construction of a counterexample which concentrates exponentially on a closed geodesic. In a second part of the paper, we prove that this model can be obtained as the limit of the three dimensional Schr\\"odinger-Poisson system, singularly perturbed by an external potential that confines the particles in the vicinity of the sphere.

In constructing a time histogram of the event sequences derived from a nonstationary point process, we wish to determine the bin width such that the mean squared error of the histogram from the underlying rate of occurrence is minimized. We find that the optimal bin widths obtained for a doubly stochastic Poisson process and a sinusoidally regulated Poisson process exhibit different scaling relations with respect to the number of sequences, time scale and amplitude of rate modulation, but both diverge under similar parametric conditions. This implies that under these conditions, no determination of the time-dependent rate can be made. We also apply the kernel method to these point processes, and find that the optimal kernels do not exhibit any critical phenomena, unlike the time histogram method.

In this paper, two parametric probability distributions capable to describe the statistics of X-ray photon detection by a CCD are presented. They are formulated from simple models that account for the pile-up phenomenon, in which two or more photons are counted as one. These models are based on the Poisson process, but they have an extra parameter which includes all the detailed mechanisms of the pile-up process that must be fitted to the data statistics simultaneously with the rate parameter. The new probability distributions, one for number of counts per time bins (Poisson-like), and the other for waiting times (exponential-like) are tested fitting them to statistics of real data, and between them through numerical simulations, and their results are analyzed and compared. The probability distributions presented here can be used as background statistical models to derive likelihood functions for statistical methods in signal analysis.

In constructing a time histogram of the event sequences derived from a nonstationary point process, we wish to determine the bin width such that the mean squared error of the histogram from the underlying rate of occurrence is minimized. We find that the optimal bin widths obtained for a doubly stochastic Poisson process and a sinusoidally regulated Poisson process exhibit different scaling relations with respect to the number of sequences, time scale and amplitude of rate modulation, but both diverge under similar parametric conditions. This implies that under these conditions, no determination of the time-dependent rate can be made. We also apply the kernel method to these point processes, and find that the optimal kernels do not exhibit any critical phenomena, unlike the time histogram method.

We show that the specific operators V^a appearing in the triplectic formalism can be viewed as the anti-Hamiltonian vector fields generated by a second rank irreducible Sp(2) tensor. This allows for an explicit realization of the triplectic algebra being constructed from an arbitrary Poisson bracket on the space of the fields only. We show that the whole space of fields and antifields can be equipped with an even supersymplectic structure when this Poisson bracket is non-degenerate. This observation opens the possibility to provide the BRST/antiBRST path integral by a well-defined integration measure, as well as to establish a direct link between the Sp(2) symmetric Lagrangian and Hamiltonian BRST quantization schemes.

Motivated by a problem on fitting multivariate models to traffic accident data, a detailed discussion of the Multivariate Poisson Lognormal (MPL) model is presented. This paper reveals three critical elements on fitting the MPL model: the setting of initial estimates, hyperparameters and tuning parameters. These issues have not been highlighted in the literature. Based on simulation studies conducted, we have shown that to use the Univariate Poisson Model (UPM) estimates as starting values, at least 20,000 iterations are needed to obtain reliable final estimates. We also illustrated the sensitivity of the specific hyperparameter, which if it is not given extra attention, may affect the final estimates. The last issue is regarding the tuning parameters where they depend on the acceptance rate. Finally, a heuristic algorithm to fit the MPL model is presented. This acts as a guide to ensure that the model works satisfactorily given any data set.

We present an efficient discontinuous Galerkin scheme for simulation of the incompressible Navier-Stokes equations including laminar and turbulent flow. We consider a semi-explicit high-order velocity-correction method for time integration as well as nodal equal-order discretizations for velocity and pressure. The non-linear convective term is treated explicitly while a linear system is solved for the pressure Poisson equation and the viscous term. The key feature of our solver is a consistent penalty term reducing the local divergence error in order to overcome recently reported instabilities in spatially under-resolved high-Reynolds-number flows as well as small time steps. This penalty method is similar to the grad-div stabilization widely used in continuous finite elements. We further review and compare our method to several other techniques recently proposed in literature to stabilize the method for such flow configurations. The solver is specifically designed for large-scale computations through matrix-...

Theoretical background and several basic test cases are presented for a new, time dependent Navier-Stokes solver for two-dimensional and axisymmetric flows. The goal of the effort is to invoke state-of-the-art computational fluid dynamics (CFD) technology to improve modeling of viscous phenomenal and to increase the robustness of CFD analysis. The original motivation was inadequate representation of supersonic ramp-induced separation by existing CFD codes. The present work addresses that inadequacy by using modern numerical methods which accurately model signal propagation in high-speed fluid flow. This technique solves the Navier-Stokes equations in general curvilinear coordinates in a four-sided domain bounded by a wall, and upper boundary opposite the wall, an inflow boundary, and an outflow boundary. The interior algorithm is a flux-difference splitting method similar to that of Yang, Lombard, and Bershader, but is blended into a second order, implicit factored delta form. With implicitly treated boundary conditions, the solution is performed using a block tridiagonal method followed by an explicit updating of the boundaries. The resulting scheme satisfies the global conversation requirement to within the order of accuracy of the algorithm. The grid is generated using a relaxation Poissonsolver. A systematic and rigorous development of the complete method is presented. Initial steps in code validation include successful reproduction of Couette and Blasius solutions.

The report presents basic statistical methods for analyzing Poisson data, such as the member of events in some period of time. It gives point estimates, confidence intervals, and Bayesian intervals for the rate of occurrence per unit of time. It shows how to compare subsets of the data, both graphically and by statistical tests, and how to look for trends in time. It presents a compound model when the rate of occurrence varies randomly. Examples and SAS programs are given.

We demonstrate that a sequence of dated mass transport deposits (MTDs) can provide information to statistically test whether or not submarine landslides associated with these deposits conform to a Poisson model of occurrence. Probabilistic tsunami hazard analysis (PTHA) most often assumes Poissonian occurrence for all sources, with an exponential distribution of return times. Using dates that define the bounds of individual MTDs, we first describe likelihood and Monte Carlo methods of parameter estimation for a suite of candidate occurrence models (Poisson, lognormal, gamma, Brownian Passage Time). In addition to age-dating uncertainty, both methods incorporate uncertainty caused by the open time intervals: i.e., before the first and after the last event to the present. Accounting for these open intervals is critical when there are a small number of observed events. The optimal occurrence model is selected according to both the Akaike Information Criteria (AIC) and Akaike's Bayesian Information Criterion (ABIC). In addition, the likelihood ratio test can be performed on occurrence models from the same family: e.g., the gamma model relative to the exponential model of return time distribution. Parameter estimation, model selection, and hypothesis testing are performed on data from two IODP holes in the northern Gulf of Mexico that penetrated a total of 14 MTDs, some of which are correlated between the two holes. Each of these events has been assigned an age based on microfossil zonations and magnetostratigraphic datums. Results from these sites indicate that the Poisson assumption is likely valid. However, parameter estimation results using the likelihood method for one of the sites suggest that the events may have occurred quasi-periodically. Methods developed in this study provide tools with which one can determine both the rate of occurrence and the statistical validity of the Poisson assumption when submarine landslides are included in PTHA.

Concentration inequalities are obtained on Poisson space, for random functionals with finite or infinite variance. In particular, dimension free tail estimates and exponential integrability results are given for the Euclidean norm of vectors of independent functionals. In the finite variance case these results are applied to infinitely divisible random variables such as quadratic Wiener functionals, including L\\'evy's stochastic area and the square norm of Brownian paths. In the infinite vari...

unclassified b. ABSTRACT unclassified c. THIS PAGE unclassified Translated Poisson Mixture Model for Stratification Learning Gloria Haro Dept. Teoria ...Pless. Figure 1 shows, for each algorithm, the point cloud with each point colored and marked differently according to its classification. In the dif...1: Clustering of a spiral and a plane. Results with different algorithms (this is a color figure). Due to the statistical nature of the R-TPMM

A system subject to a point process of shocks is considered. Shocks occur in accordance with the homogeneous Poisson process. Different criteria of system failure (termination) are discussed and the corresponding probabilities of failure (accident)-free performance are derived. The described analytical approach is based on deriving integral equations for each setting and solving these equations through the Laplace transform. Some approximations are analyzed and further generalizations and applications are discussed.

In section 2 we describe more carefully the generalized Poisson processes, giving a realization of the underlying probability space, and we characterize these processes by their characteristic functionals. Section 3 is devoted to the proof of the previous formula for quantum mechanical systems, with possibly velocity dependent potentials and in section 4 we give an application of the previous theory to some relativistic Bose field models.

In order to check the distortions, introduced by a non-extended dead time on the Poisson statistics, accurate experiments have been made in single channel counting. At a given measuring time, the dependence on the choice of the time origin and on the width of the dead time has been verified. An excellent agreement has been found between the theoretical expressions and the experimental curves.

In order to check the distortions, introduced by a non-extended dead time on the Poisson statistics, accurate experiments have been made in single channel counting. At a given measuring time, the dependence on the choice of the time origin and on the width of the dead time has been verified. An excellent agreement has been found between the theoretical expressions and the experimental curves.

We discuss the A-model as a gauge fixing of the Poisson Sigma Model with target a symplectic structure. We complete the discussion in [4], where a gauge fixing defined by a compatible complex structure was introduced, by showing how to recover the A-model hierarchy of observables in terms of the AKSZ observables. Moreover, we discuss the off-shell supersymmetry of the A-model as a residual BV symmetry of the gauge fixed PSM action.

Semi-Poisson statistics are shown to be obtained by removing every other number from a random sequence. Retaining every (r+1)th level we obtain a family of secuences which we call daisy models. Their statistical properties coincide with those of Bogomolny's nearest-neighbour interaction Coulomb gas if the inverse temperature coincides with the integer r. In particular the case r=2 reproduces closely the statistics of quasi-optimal solutions of the traveling salesman problem.

Full Text Available The group-buying is the modern business of selling in the uncertain market. With an objective to minimize costs for sellers arising from ordering and reordering, we present in this paper the group buying inventory model, with the demand governed by a Poisson process and the product sale distributed as Binomial distribution. The inventory level is under continuous review, while the lead time is fixed. A numerical example is illustrated.

The purpose of this report is to outline code and solution verification activities applied to HIGRAD, a Computational Fluid Dynamics (CFD) solver of the compressible Navier-Stokes equations developed at the Los Alamos National Laboratory, and used to simulate various phenomena such as the propagation of wildfires and atmospheric hydrodynamics. Code verification efforts, as described in this report, are an important first step to establish the credibility of numerical simulations. They provide evidence that the mathematical formulation is properly implemented without significant mistakes that would adversely impact the application of interest. Highly accurate analytical solutions are derived for four code verification test problems that exercise different aspects of the code. These test problems are referred to as: (i) the quiet start, (ii) the passive advection, (iii) the passive diffusion, and (iv) the piston-like problem. These problems are simulated using HIGRAD with different levels of mesh discretization and the numerical solutions are compared to their analytical counterparts. In addition, the rates of convergence are estimated to verify the numerical performance of the solver. The first three test problems produce numerical approximations as expected. The fourth test problem (piston-like) indicates the extent to which the code is able to simulate a 'mild' discontinuity, which is a condition that would typically be better handled by a Lagrangian formulation. The current investigation concludes that the numerical implementation of the solver performs as expected. The quality of solutions is sufficient to provide credible simulations of fluid flows around wind turbines. The main caveat associated to these findings is the low coverage provided by these four problems, and somewhat limited verification activities. A more comprehensive evaluation of HIGRAD may be beneficial for future studies.